FMCW cable insulation defect detection method based on live working condition equivalent simulation
By using equivalent simulation technology and FMCW method under live conditions, the problem of poor positioning accuracy of cable insulation defect detection is solved, and more efficient cable fault positioning and grid reliability are achieved.
Patent Information
- Application Number
- CN202411939342.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-26
- Publication Date
- 2025-05-16
AI Technical Summary
The existing methods for detecting insulation defects of cables with live operating conditions have the problem of poor positioning accuracy, especially in complex environments of cable connection equipment.
The FMCW cable insulation defect detection method based on live operating conditions is adopted. By establishing a cable distribution parameter model and an equivalent simulation circuit for actual operating conditions, an FMCW cable defect detection and positioning experimental platform under live operating conditions is built, and the cable transmission signals are adjusted in real time to obtain the frequency difference, and defect point positioning is used using the frequency difference and current voltage parameters.
It improves the positioning accuracy and detection efficiency of cable insulation defect detection under live conditions, is suitable for cable fault detection and positioning in different on-site environments, reduces losses caused by cable power outages, and improves the reliability of the power grid.
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Figure CN120009673A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of power equipment defect detection. Background Art
[0002] With the development of society, the demand for electric power resources in various fields is increasing, and the transmission and distribution network is becoming increasingly large. Once insulation defects occur, they often cause irreparable impacts. Effective detection of cables is of great significance to improving the reliability of the power grid. A method for locating local defects in cables based on frequency modulated continuous wave (FMCW) has better noise resistance and a longer detection distance than the traditional broadband impedance spectroscopy (BIS) measurement amplitude because its measurement principle is the frequency difference between the incident signal and the reflected signal caused by time delay. However, this method currently lacks research on the impact of live working conditions on the positioning of this method, and only stays in the offline detection of cable monomers, which has the problem of poor detection accuracy under live working conditions. Summary of the invention
[0003] The present invention aims to solve the problem of poor defect point positioning accuracy in existing live working condition cable insulation defect detection, and provides a FMCW cable insulation defect detection method based on equivalent simulation of live working conditions.
[0004] The FMCW cable insulation defect detection method based on equivalent simulation of live working conditions of the present invention comprises:
[0005] S1. According to the transmission line theory and the principle of cable signal propagation process, a distributed parameter model of the power cable is established; the characteristic impedance of the cable, the signals at different positions of the cable, and the propagation constant and reflection coefficient of the signal in the cable are obtained;
[0006] Obtain actual working conditions and establish equivalent simulation circuits of cable connection equipment in actual working conditions;
[0007] S2. Using the distributed parameter model of the cable, the characteristic impedance of the cable, the signal wave propagation constant and the reflection coefficient at different positions of the cable, an FMCW cable defect live detection and positioning experimental platform under live working conditions is constructed, and the cable transmission signal acquisition mode of the experimental platform is set to the cable outer ring capacitance coupling injection mode;
[0008] S3, adjusting the cable transmission signal in real time to obtain the frequency difference between the injected signal and the reflected signal in the cable;
[0009] The frequency difference and current and voltage parameters in actual working conditions are utilized, and the FMCW cable defect detection method is adopted to obtain the defect point location.
[0010] Furthermore, in the present invention, in S1, the distributed parameter model of the power cable established is:
[0011]
[0012] Where: ω = 2πf is the angular frequency; r c and r s are the cable core radius and the inner radius of the shielding layer respectively; ρ c and ρ s are the resistivity of the cable core and shielding layer respectively; μ0 is the vacuum permeability; ε and σ are the dielectric constant and conductivity of the dielectric respectively, R0, L0, G0, C0 are the resistance, inductance, conductance and capacitance of the cable per unit length respectively.
[0013] Furthermore, in the present invention, in S1, the signals at different positions of the cable are:
[0014] V(k)=V i2 e γ(l-k) +V r2 e -γ(l-k)
[0015]
[0016] Where V i2 is the incident voltage wave on the load side; V r2 is the reflected voltage wave on the load side; γ is the propagation constant of the signal in the cable; Z0 is the characteristic impedance of the cable, l is the total length of the cable, V(k) is the voltage at any position k away from the beginning of the cable, and I(k) is the current at any position k away from the beginning of the cable.
[0017] Further, in the present invention, in S1, the propagation constant of the signal in the cable is expressed by the formula:
[0018]
[0019] Obtained, where α is the attenuation constant; β is the phase constant; v is the propagation speed of electromagnetic waves in the cable; ω is the angular frequency; f is the frequency, and j is the imaginary unit.
[0020] Furthermore, in the present invention, in S1, the characteristic impedance of the cable is obtained as follows:
[0021] Since ωL0>>R0, ωC0>>G0, the characteristic impedance Z0 is obtained by the formula:
[0022]
[0023] Wherein, Z0(ω) is the characteristic impedance of the cable when the angular frequency of the signal in the cable is ω.
[0024] Further, in the present invention, in S1, the propagation constant is expressed by the formula:
[0025]
[0026] Get, where Z L is the load impedance, Γ(k) is the reflection coefficient at any position k; the reflection coefficient at the end of the line is:
[0027]
[0028] Further, in the present invention, in S2, the frequency difference between the injected signal and the reflected signal in the cable is:
[0029]
[0030] Where f(t) is the frequency of the signal injected into the cable, f r (t) is the frequency of the reflected signal, t and μ respectively control the duration and bandwidth of the signal, t d =2D / v is the two-way delay to the fault target, D is the distance of the fault target from the signal transmitter, and v is the transmission speed of the signal in the cable.
[0031]
[0032] Where ω0(t) is the injected signal V in the cable. i2 The angular frequency of the circuit is f0, and f0 is the center frequency.
[0033] Furthermore, in the present invention, in S3, the formula for obtaining the defect point position is:
[0034]
[0035] Wherein, Δf is half bandwidth of frequency modulation; Ts is period of frequency modulation.
[0036] Compared with the existing method for detecting and locating local insulation defects of cables based on frequency modulated continuous wave, the present invention simulates the connection of electrical equipment in the actual working conditions of the cable, uses equivalent circuit model simulation substitution, and builds experimental platforms under different environmental types, so that the local insulation defect detection method of cables based on FMCW is more suitable for detection and positioning under live working conditions, modulates reasonable signal parameters in advance, saves time for dealing with complex situations on site, and improves the efficiency of on-site detection. The online positioning monitoring of live cables based on this invention proposes a new solution for online monitoring of urban distribution cables, avoids unnecessary losses caused by cable power outages, improves detection efficiency, and has great significance for the development of power grid reliability. BRIEF DESCRIPTION OF THE DRAWINGS
[0037] Figure 1is a flow chart of the method of the present invention;
[0038] Figure 2 It is a transformer equivalent circuit model diagram in a specific implementation mode;
[0039] Figure 3 It is a schematic diagram of cable connection under actual live working conditions simulated in a specific implementation manner;
[0040] Figure 4 It is a cable distribution parameter model diagram in a specific implementation method. DETAILED DESCRIPTION
[0041] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.
[0042] Specific implementation method 1: refer to Figure 1 Specifically describing this embodiment, the FMCW cable insulation defect detection method based on equivalent simulation of live working conditions described in this embodiment includes:
[0043] S1. According to the transmission line theory and the principle of cable signal propagation process, a distributed parameter model of the power cable is established; the characteristic impedance of the cable, the signals at different positions of the cable, and the propagation constant and reflection coefficient of the signal in the cable are obtained;
[0044] Obtain actual working conditions and establish equivalent simulation circuits of cable connection equipment in actual working conditions;
[0045] S2. Using the distributed parameter model of the cable, the characteristic impedance of the cable, the signal wave propagation constant and the reflection coefficient at different positions of the cable, an FMCW cable defect live detection and positioning experimental platform under live working conditions is constructed, and the cable transmission signal acquisition mode of the experimental platform is set to the cable outer ring capacitance coupling injection mode;
[0046] S3, adjusting the cable transmission signal in real time to obtain the frequency difference between the injected signal and the reflected signal in the cable;
[0047] The frequency difference and current and voltage parameters in actual working conditions are utilized, and the FMCW cable defect detection method is adopted to obtain the defect point location.
[0048] Furthermore, in the present invention, in S1, the distributed parameter model of the power cable established is:
[0049]
[0050] Where: ω = 2πf is the angular frequency; r c and r s are the cable core radius and the inner radius of the shielding layer respectively; ρ c and ρ s are the resistivity of the cable core and shielding layer respectively; μ0 is the vacuum permeability; ε and σ are the dielectric constant and conductivity of the dielectric respectively, R0, L0, G0, C0 are the resistance, inductance, conductance and capacitance of the cable per unit length respectively.
[0051] Furthermore, in the present invention, in S1, the signals at different positions of the cable are:
[0052] V(k)=V i2 e γ(l-k) +V r2 e -γ(l-k)
[0053]
[0054] Where V i2 is the incident voltage wave on the load side; V r2 is the reflected voltage wave on the load side; γ is the propagation constant of the signal in the cable; Z0 is the characteristic impedance of the cable, l is the total length of the cable, V(k) is the voltage at any position k away from the beginning of the cable, and I(k) is the current at any position k away from the beginning of the cable.
[0055] Further, in the present invention, in S1, the propagation constant of the signal in the cable is expressed by the formula:
[0056]
[0057] Obtained, where α is the attenuation constant; β is the phase constant; v is the propagation speed of electromagnetic waves in the cable; ω is the angular frequency; f is the frequency, and j is the imaginary unit.
[0058] Furthermore, in the present invention, in S1, the characteristic impedance of the cable is obtained as follows:
[0059] Since ωL0>>R0, ωC0>>G0, the characteristic impedance Z0 is obtained by the formula:
[0060]
[0061] Wherein, Z0(ω) is the characteristic impedance of the cable when the angular frequency of the signal in the cable is ω.
[0062] Further, in the present invention, in S1, the propagation constant is expressed by the formula:
[0063]
[0064] Get, where Z L is the load impedance, Γ(k) is the reflection coefficient at any position k; the reflection coefficient at the end of the line is:
[0065]
[0066] Further, in the present invention, in S2, the frequency difference between the injected signal and the reflected signal in the cable is:
[0067]
[0068] Where f(t) is the frequency of the signal injected into the cable, f r (t) is the frequency of the reflected signal, t and μ respectively control the duration and bandwidth of the signal, t d =2D / v is the two-way delay to the fault target, D is the distance of the fault target from the signal transmitter, and v is the transmission speed of the signal in the cable.
[0069]
[0070] Where ω0(t) is the injected signal V in the cable. i2 The angular frequency of the circuit is f0, and f0 is the center frequency.
[0071] Furthermore, in the present invention, in S3, the formula for obtaining the defect point position is:
[0072]
[0073] Wherein, Δf is half bandwidth of frequency modulation; Ts is period of frequency modulation.
[0074] The present invention provides an equivalent simulation method for live detection of cable insulation defects based on FMCW. The working principle is as follows: by simulating the distribution cable connection conditions (switch cabinets, transformers, etc.) in actual working conditions, using equivalent circuits to convert electrical equipment, building an experimental platform for analysis based on a cable distribution parameter model, and designing FMCW live detection and positioning under cable-connected electrical equipment, thereby studying the influence of cable-connected electrical equipment on FMCW local insulation defect live detection and positioning, and realizing cable fault detection and positioning suitable for different field environments.
[0075] The specific implementation method is: due to the different electrical parameters in the cable, the reflection signal response is different, which will eventually affect the FMCW positioning spectrum line. The positioning spectrum line characteristics of the cable connected to different electrical equipment are measured, and the spectrum line characteristics, especially the characteristics of the positioning peak, are analyzed. Finally, the positioning characteristics of typical defects are obtained to propose a criterion to realize the online monitoring of FMCW cable insulation defects under live working conditions.
[0076] The advantage of the present invention is that it utilizes an analog circuit model to solve key practical problems that need to be solved on site when the FMCW method is applied to online monitoring, studies the influence of cable-connected electrical equipment on the positioning result of the method under live conditions, provides a basis for conducting research on live detection of local insulation defects of cables using the FMCW method, provides reasonable modulation parameters for cable fault detection and positioning suitable for different field environments, greatly improves the reliability of cable online monitoring, and helps to improve the stability and economy of power grid operation.
[0077] Transformers are commonly used in power systems and are of great significance to the transmission and distribution of electric energy. They are devices that use the principle of electromagnetic induction to change AC voltage. The main components are primary coils, secondary coils, and iron cores (magnetic cores). The main functions include: voltage conversion, current conversion, impedance conversion, isolation, voltage stabilization (magnetic saturation transformer), etc.
[0078] The main function of the switch cabinet is to open and close, control and protect electrical equipment in the process of power generation, transmission, distribution and power conversion in the power system. The components in the switch cabinet mainly include circuit breakers, disconnectors, load switches, operating mechanisms, mutual inductors and various protection devices. The external line of the switch cabinet first enters the main control switch in the cabinet, and then enters the sub-control switch. Each branch is set according to its needs.
[0079] According to the transmission line theory, a distributed parameter model of power cables can be established to describe the transmission process of energy and signals in cables. Figure 3 As shown in the figure: R0, L0, G0, C0 are the resistance, inductance, conductance and capacitance of the cable per unit length respectively. The calculation of cable distribution parameters is shown in the formula:
[0080]
[0081] Where: ω = 2πf is the angular frequency; r c and r s are the cable core radius and the inner radius of the shielding layer respectively; ρ c and ρ s are the resistivity of the cable core and shielding layer respectively; μ0 is the magnetic permeability of vacuum; ε and σ are the dielectric constant and conductivity of the dielectric respectively.
[0082] Assuming that the total length of the cable is l, according to the cable equivalent circuit, the voltage V(k) and current I(k) at any position k from the beginning of the cable can be obtained as follows:
[0083] V(k)=V i2 e γ(l-k) +V r2 e -γ(l-k)
[0084]
[0085] Where: V i2 is the incident voltage wave on the load side; V r2 is the reflected voltage wave on the load side; γ is the propagation constant of the cable; Z0 is the characteristic impedance of the cable. The propagation constant γ is:
[0086]
[0087] Where: α is the attenuation constant; β is the phase constant; v is the propagation speed of electromagnetic waves in the cable; ω is the angular frequency; f is the frequency. At high frequencies, since ωL0>>R0, ωC0>>G0, the characteristic impedance Z0 is:
[0088]
[0089] In a power cable with a length of l, the reflection coefficient at any position k is defined as:
[0090]
[0091] Where: Z L is the load impedance. From this, the reflection coefficient at the end of the line is:
[0092]
[0093] In actual cable lines, due to external force damage or insulation aging, the cable will form local defects, causing changes in various electrical parameters. At this time, a series of refractions and reflections will be formed when the signal passes through the line. When the end of the line is open, that is, Z L =∞, the reflection coefficient, Г(k) can be expressed as:
[0094] Γ(k)=e -2γ(l-k) =e -2α(l-k) e -2jβ(l-k)
[0095] The location information of the defect point can be obtained by performing FMCW experimental analysis on the cable distributed parameter model. The signal after frequency difference processing is analyzed and processed using fast Fourier transform (FFT). The cable defect and the end can be located by finding the position corresponding to the reflection at the local defect and the end of the cable.
[0096] In the present invention, the cable transmission signal is adjusted in real time to obtain the frequency difference between the injected signal and the reflected signal in the cable;
[0097] The specific process of obtaining the defect point location by using the FMCW cable defect detection method using the frequency difference and the current and voltage parameters in the actual working condition is as follows:
[0098] Since the signal used by FMCW is a linear frequency modulation (LFM) signal, the LFM waveform has the following expression in the time domain:
[0099]
[0100] Where: A is the signal amplitude; frect(t / τ) represents a rectangular pulse with a width of τ; f0 is the center frequency; t and μ control the duration and bandwidth of the signal respectively. In the frequency domain, V i2 The continuous waveform of the signal is transmitted in a sawtooth shape and can be written as follows:
[0101]
[0102] Where: ω0(t) is V i2 Angular frequency of the cosine signal; V i2 The initial phase of the signal. i2 The frequency f of the signal can be calculated as follows:
[0103]
[0104] Assume that the signal V i2 The distance to the impedance mismatch point is D, and the received signal V r2 It can be calculated as:
[0105]
[0106] Where: α is the signal transmission attenuation factor; t d =2D / v is the two-way delay to the target, where v is the transmission speed of the signal in the cable. The average wave speed of the signal in the cable can be measured by the pulse reflection method. The frequency of the received signal f r It can be calculated as follows:
[0107]
[0108] Will accept the signal V r2 With reference signal V i2 After mixing and extracting the lower sideband, the output signal can be expressed as:
[0109]
[0110] Where: f b (t) is the frequency difference, as shown in formula (7); For signal s out phase.
[0111]
[0112] Among them, f b Mainly composed of f b + The signal composition can be obtained by the following formula:
[0113]
[0114] Where: Δf is half bandwidth of frequency modulation; Ts is frequency modulation period. Time difference signal t d Positively correlated with the target distance D and the frequency difference signal f b The target distance D can be calculated by the formula:
[0115]
[0116] In this method, the FMCW incident signal V is extracted by capacitive coupling. i2 With the reflected signal V r2 Then the mixing process is performed to obtain s out Signal, after fast Fourier transform, can calculate s out The spectrum of the signal is used to obtain the target distance D.
[0117] Based on this model, the connection of electrical equipment under energized conditions is taken into account and an equivalent circuit simulation is performed. The simulation method and the FMCW positioning method process are as follows: Figure 1 As shown. The transformer is a key link in the power distribution network system. It is an electronic component that uses the principle of mutual conversion between electricity and magnetism to realize the transfer of energy from one port to another. The basic structure is a magnetic core and two or more windings wound on the same magnetic core. The only thing connecting the two circuits is the magnetic circuit. The analysis starts from the magnetic circuit part to obtain the relationship between certain parameters of the two circuits. Then, based on the relationship, a target equivalent circuit is established. The equivalent circuit is used to convert the transformer into basic components such as resistance and inductance, and some analysis is performed with the help of basic circuit theory.
[0118] In the initial state, there is no load on the secondary side of the transformer, so the primary side generates a no-load current I0sin(wt), and the no-load current is an alternating current, so an alternating magnetic field is generated in the primary side coil to generate the main magnetic flux:
[0119] Φ m =Φ0sin(wt)
[0120] The magnetic flux in the secondary coil is constantly changing, which causes an induced electromotive force in the secondary coil. In the iron core of the transformer, due to the constantly changing magnetic field, eddy currents will be generated inside the iron core, which will generate heat and cause energy consumption. The heat here is equivalent to the equivalent resistance R of the transformer in the circuit. m The heat generated will be consumed, and secondly, it will cause the voltage to lead the current. In equivalent terms, the transformer will generate an equivalent inductance Z on the primary side. m When the load is connected, the induced electromotive force generates an induced current I2 and an induced magnetic flux Φ2sin(wt), which in turn causes the amplitude of the main magnetic flux in the transformer core to change:
[0121] Φ m =(Φ1-Φ2)sin(wt)
[0122] Next, as the amplitude of the main magnetic flux decreases, the induced electromotive force U1 generated on the primary side decreases, the voltage shared by the resistance on the primary side increases, and the current increases from the no-load current I0 to I1. Then I1 will cause the amplitude of the main magnetic flux to increase, resulting in an increase in the induced voltage on the secondary side, which in turn causes an increase in the current on the secondary side. The equivalent circuit diagram is as follows Figure 2 shown.
[0123] Switchgear is widely used in power supply systems, responsible for receiving and distributing electric energy and protecting the line safety of various electrical equipment. According to the needs of power grid operation, in the event of a fault in electrical equipment or lines, the connection with the power grid can be quickly disconnected, thereby ensuring the normal operation of the non-faulty part of the power grid and the safety of operation and maintenance personnel and equipment. In actual engineering wiring, the first end of the cable is connected to the switchgear through the busbar, and the disconnected state is equivalent to the first end of the cable being disconnected. Figure 2 In the figure, u1 is the signal injected into the line; Z1 and Z2 are the wave impedances of the primary and secondary side lines of the PT respectively; L is the inductance between the lines. The inductor is connected in series at the head end to simulate electrical equipment with different parameters, and the influence of the value of the series inductor at the head end on the reflected wave of the injected signal is studied.
[0124] The present invention carries out FMCW-based detection and positioning of multiple groups of different typical defects under the above-mentioned live simulated working conditions, analyzes the test results, measures the positioning spectral line characteristics, and analyzes its spectral line characteristics, especially the characteristics of the positioning peak, to study the influence of cable-connected electrical equipment on the live detection and positioning of FMCW local insulation defects. Finally, a criterion is proposed using the positioning characteristics of the obtained typical defects to realize online monitoring of frequency modulated continuous wave cable insulation defects under live working conditions, and realize an online detection and positioning simulation method for cable faults suitable for different field environments.
[0125] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.
Claims
1. The FMCW cable insulation defect detection method based on equivalent simulation of live working conditions is characterized by: include: S1. According to the transmission line theory and the principle of cable signal propagation process, a distributed parameter model of the power cable is established; the characteristic impedance of the cable, the signals at different positions of the cable, and the propagation constant and reflection coefficient of the signal in the cable are obtained; Obtain actual working conditions and establish equivalent simulation circuits of cable connection equipment in actual working conditions; S2. Using the distributed parameter model of the cable, the characteristic impedance of the cable, the signal wave propagation constant and the reflection coefficient at different positions of the cable, an FMCW cable defect live detection and positioning experimental platform under live working conditions is constructed, and the cable transmission signal acquisition mode of the experimental platform is set to the cable outer ring capacitance coupling injection mode; Real-time adjustment of the cable transmission signal in the FMCW cable defect live detection and positioning experimental platform to obtain the frequency difference between the injection signal and the reflection signal in the cable; S3. Utilizing the frequency difference and current and voltage parameters in actual working conditions, an FMCW cable defect detection method is adopted to obtain the defect point location.
2. The FMCW cable insulation defect detection method based on equivalent simulation of live working conditions according to claim 1 is characterized in that: In S1, the distributed parameter model of the power cable is established as: Where: ω = 2πf is the angular frequency; r c and r s are the cable core radius and the inner radius of the shielding layer respectively; ρ c and ρ s are the resistivity of the cable core and shielding layer respectively; μ0 is the vacuum permeability; ε and σ are the dielectric constant and conductivity of the dielectric respectively, R0, L0, G0, C0 are the resistance, inductance, conductance and capacitance of the cable per unit length respectively.
3. The FMCW cable insulation defect detection method based on equivalent simulation of live working conditions according to claim 2 is characterized in that: In S1, the propagation constant of the signal in the cable is given by the formula: Obtained, where α is the attenuation constant; β is the phase constant; v is the propagation speed of electromagnetic waves in the cable; ω is the angular frequency; f is the frequency, and j is the imaginary unit.
4. The FMCW cable insulation defect detection method based on equivalent simulation of live working conditions according to claim 3 is characterized in that: In S1, the process of obtaining the characteristic impedance of the cable is: Since ωL0>>R0, ωC0>>G0, the characteristic impedance Z0 is obtained by the formula: Wherein, Z0(ω) is the characteristic impedance of the cable when the angular frequency of the signal in the cable is ω.
5. The FMCW cable insulation defect detection method based on equivalent simulation of live working conditions according to claim 4 is characterized in that: In S1, the propagation constant is given by the formula: Get, where Z L is the load impedance, Γ(k) is the reflection coefficient at any position k; the reflection coefficient at the end of the line is:
6. The FMCW cable insulation defect detection method based on equivalent simulation of live working conditions according to claim 5 is characterized in that: In S2, the frequency difference between the injected signal and the reflected signal in the cable is: Where f(t) is the frequency of the signal injected into the cable, f r (t) is the frequency of the reflected signal, t and μ respectively control the duration and bandwidth of the signal, t d =2D / v is the two-way delay to the fault target, D is the distance of the fault target from the signal transmitter, and v is the transmission speed of the signal in the cable. Where ω0(t) is the signal V injected into the cable. i2 The angular frequency of the circuit is f0, and f0 is the center frequency.
7. The FMCW cable insulation defect detection method based on equivalent simulation of live working conditions according to claim 6 is characterized in that: In S3, the formula for obtaining the defect point position is: Wherein, Δf is half bandwidth of frequency modulation; Ts is period of frequency modulation.
Citation Information
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