CN114414947A - Head end impedance matching method suitable for FDR test and cable impedance mismatching position reflection state evaluation method - Google Patents

Head end impedance matching method suitable for FDR test and cable impedance mismatching position reflection state evaluation method Download PDF

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CN114414947A
CN114414947A CN202210006066.6A CN202210006066A CN114414947A CN 114414947 A CN114414947 A CN 114414947A CN 202210006066 A CN202210006066 A CN 202210006066A CN 114414947 A CN114414947 A CN 114414947A
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impedance
cable
reflection
head end
reflection coefficient
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CN114414947B (en
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周凯
谢敏
唐志荣
孟鹏飞
黄靖涛
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Sichuan University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/11—Locating faults in cables, transmission lines, or networks using pulse reflection methods
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
    • G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
    • G01R27/16—Measuring impedance of element or network through which a current is passing from another source, e.g. cable, power line
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
    • G01R31/083—Locating faults in cables, transmission lines, or networks according to type of conductors in cables, e.g. underground
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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Abstract

The invention discloses a head end impedance matching method suitable for FDR (fully drawn wire) test, which introduces a variable resistor ZsEffectively calculating the reflection coefficient of the head end of the cable and the characteristic impedance of the cable to obtain the input impedance Z of the head end of the cableinTherefore, effective correction of field FDR data is achieved, and the influence of impedance mismatching of the head end caused by stray parameters of the branched lead on a test result is restrained; and the reflection coefficient under the condition of impedance matching of the head end of the cable can be further obtained. On the basis of realizing the impedance matching of the head end, the invention can further realize the effective judgment of the reflection type and the reflection polarity of the impedance mismatching position of the cable, and can further obtain the reflection coefficient of the impedance mismatching position of the cable, thereby providing guiding significance for the practical application of the FDR in the field.

Description

Head end impedance matching method suitable for FDR test and cable impedance mismatching position reflection state evaluation method
Technical Field
The invention belongs to the field of state monitoring and fault diagnosis of power equipment, relates to the reflection state evaluation of a cable intermediate joint, and particularly relates to a reflection state evaluation technology for a cable impedance mismatching position based on FDR and impedance matching.
Background
FDR (frequency Domain reflectometer) frequency Domain reflection technology is characterized in that a sweep frequency test signal of a specific frequency band is sent, reflection signals which are stronger and have the same frequency as a transmission signal but different time periods are generated at the position where the impedance of a conductor is mismatched, the signals are analyzed in a Fourier conversion mode, and the distance of a line obstacle point is converted by measuring the frequency of a peak value of the reflection signal. This technique has been applied to the field of communication testing. The conventional FDR method has begun to be widely used for cable insulation state diagnosis due to a longer test range and higher test sensitivity.
However, this method does not take into account the effect of the impedance mismatch at the head end of the cable on the test results, which results in significant distortion of the test waveform, and it cannot be calibrated directly by the calibration procedure of the VNA. Meanwhile, a relative ratio method is adopted for diagnosis and analysis (test data of intact cables needs to be provided), so that the evaluation result has certain limitation, namely the reflection intensity at the position of the middle joint of the cable cannot be truly reflected. In addition, in the field test using FDR, since the reflection polarity at the cable intermediate connector position cannot be determined well, the insulation defect type at the cable intermediate connector position cannot be identified accurately.
Disclosure of Invention
The invention aims to provide a head end impedance matching method to solve the problem that the testing effect is influenced by the mismatching of the head end impedance of a cable.
The invention further aims to provide a cable impedance mismatching position reflection state evaluation method based on the head end impedance matching method, which can realize the judgment of the reflection polarity and the reflection type of the intermediate joint.
In order to achieve the purpose, the invention adopts the following technical scheme to realize.
According to the head end impedance matching method, the head end reflection coefficient gamma under FDR is obtained firstly0And (omega), further obtaining the input impedance of the cable, thereby effectively inhibiting the influence of the stray parameters of the branched leads on the test result. And then, the effective judgment of the reflection type and the reflection polarity of the impedance mismatching position is realized by using a trigonometric function superposition method, and the effective compensation of attenuation is realized by using a linear function in a logarithmic coordinate, so that the reflection coefficient of the impedance mismatching position is obtained.
From the traveling wave theory, it can be seen that the FDR expression U obtained from the cable head end test in the case where there is an impedance mismatch and the reflection at the cable end is ignored for the power cable given in fig. 11(ω) can be expressed as:
Figure BDA0003456783040000021
in the formula of U0(ω) is the injection signal; ω 2 pi f is the angular frequency; f is the test frequency; rho1The reflection coefficient of the head end of the cable (without considering the reflection condition of other positions of the cable) can be expressed as rho1＝(Z0-R0)/(Z0+R0)，Z0Is the characteristic impedance, R, of the cable0Is the characteristic impedance of the coaxial cable connected between the tester and the cable; rho2The reflection coefficient of the end face of the cable body and the impedance mismatch position can be expressed as rho2＝(Z1-Z0)/(Z1+Z0)，Z1Characteristic impedance of the impedance mismatch location; gamma is the propagation constant of the cable, gamma1Is the propagation constant of the cable impedance mismatch location; l1Representing the distance from the cable impedance mismatch location to the cable head end, d the length of the impedance mismatch location. When the cable has an impedance mismatch position, the signal generates a plurality of refraction and reflection phenomena in the impedance mismatch position, so that the waveform reflected to the head end of the cable from the impedance mismatch position is obviously distorted.
Reflection coefficient gamma of cable head end calculated by impedance method0(ω) is represented by formula (2):
Figure BDA0003456783040000022
in the formula, ZinAnd (omega) is the input impedance at the head end of the cable.
In performing FDR testing of field cables, the test method shown in FIG. 2 is typically employed for testing. The characteristic impedance of the coaxial cable is consistent with the internal resistance of a Vector Network Analyzer (VNA). As can be seen from fig. 1, under the influence of stray parameters of the cable terminal and the test branch lead, the measured result will include the stray parameters and the cable parameters, which results in a significant distortion of the test waveform. As shown in fig. 3, when there is no bifurcated lead, the real part of the reflection coefficient obtained by the test is a more regular cosine attenuation function; when the branched lead exists, the real part of the reflection coefficient fluctuates obviously, so that the influence of the stray parameters of the branched lead on the test result is large.
Since the stray parameters of the branched leads have a large influence on the test result and cannot be calibrated directly by using the calibration procedure of the VNA, the present invention proposes to use the variable series impedance Z to eliminate the influence of the test leadssThe split lead position stray parameter was modeled as shown in fig. 4.
The combination formula (2) can obtain the reflection coefficient gamma of the head end of the cable obtained by the impedance method0(ω) is represented by the formula (3).
Figure BDA0003456783040000023
In formula (II), Z'inAnd (omega) is the input impedance of the head end of the cable measured by the tester.
Further, based on the previous FDR expression U1(ω), ρ can be calculated1As shown in formula (4):
Figure BDA0003456783040000024
obtaining a variable series impedance Z from equation (4)sAs shown in formula (5):
Figure BDA0003456783040000031
from the equation (5), when ρ is known1And a characteristic impedance Z0Then, the variable series impedance Z can be calculated by the formula (5)sFurther, the input impedance Z of the head end of the cable can be calculated by using the formula (3)inTherefore, the influence of the stray parameters of the branched lead on the test result is effectively inhibited. Thus, ρ1And a characteristic impedance Z0Is the key to achieving the stray parameter suppression of the bifurcated lead.
Based on the above analysis, the present invention provides a head end impedance matching method suitable for FDR testing, comprising the steps of:
s1 takes Gaussian pulse as incident signal, FDR test is carried out on the cable connected with the branch lead to obtain the reflection coefficient gamma of the head end of the cable0(omega), then acquiring frequency domain reflection signals according to the reflection coefficients and the Gaussian pulse signals respectively; then obtaining a reflection coefficient rho of the head end of the cable according to a first reflection pulse signal and a Gaussian pulse signal obtained by frequency domain reflection signals1；
S2 obtaining the characteristic impedance Z of the cable by adopting an enumeration method0；
S3 reflection coefficient rho according to head end of cable1Characteristic impedance Z of cable0Obtaining a variable series impedance Z according to equation (5)s；
S4 based on variable series impedance ZsCalculating the input impedance Z of the head end of the cable according to the formula (3)in。
In the above step S1, the present invention introduces Gaussian pulse as the incident signal and then uses the reflection coefficient Γ0(omega) calculating to obtain a time domain reflection signal, and finally extracting a first reflection pulse to realize rho1Obtaining the target value. The method specifically comprises the following steps:
s11 using Gaussian pulse as incident signal, measuring the ratio of the reflected signal and incident signal at the head end by the tester to obtain the reflection coefficient gamma of the head end of the cable0(ω)；
S12 generating the Gaussian pulse signal y using the following formula0(t)：
Figure BDA0003456783040000032
In the formula, w is the Gaussian pulse width; t is time;
s13 pairs of Gaussian pulse signals y0(t) performing Fast Fourier Transform (FFT) processing to obtain Y0(ω)；
S14, calculating to obtain the frequency domain expression Y of the reflected signal by using the following formula1(ω)：
Y1(ω)＝Y0(ω)·Γ0(ω) (8)
S15 pair of reflected signals Y1(omega) performing Inverse Fast Fourier Transform (IFFT) processing to obtain y1(t)；
S16 intercepting y by time window1(t) first reflection pulse y2(t)；
S17 for the first reflected pulse y2(t) FFT processing to obtain Y2(ω)；
S18 is calculated by the following formula1：
Figure BDA0003456783040000041
It should be noted that, since the stray parameter of the head-end branched lead is a variation, ρ cannot be directly calculated by directly using the signal intensity of the head-end reflected pulse1。
Further analysis of equation (3) reveals that variable series impedance Z is assumedsIt is known and is derived from Z'inElimination in (omega) (to obtain Zin(omega)), at the moment, if the signal source internal resistance value is replaced by the cable characteristic impedance Z0Then, the reflection coefficient gamma under the condition of head end impedance matching can be calculated by the formula (3)1(ω)：
Figure BDA0003456783040000042
From the above analysis and the formula (5), when ρ is1When known, the characteristic impedance Z of the cable is calculated0Therefore, the impedance matching of the head end of the cable can be realized. Normally, the characteristic impedance Z of the cable0Can be approximated by a constant. Therefore, the invention realizes the characteristic impedance Z of the cable in an enumeration mode0Obtaining the target value. Step S2 therefore includes the following substeps:
s21 gives an assumed characteristic impedance, and gives an assumed characteristic impedance Z0·kAssigning the initial value of (a), wherein k represents the cycle number;
s22 variable series impedance Z under the assumed characteristic impedance is calculated by formula (5)s；
S23 calculating input impedance Z under head end impedance matching condition by using formula (10)in(ω)；
S24 for ZinPerforming FFT processing on the phase of (omega), only retaining data of the cable terminal position, and performing IFFT processing on other data by setting zero;
s25 comparing the first M cycles and Z of the data obtained by IFFT processing in step S24inComparing the first M periods of the (omega) phase and obtaining the Pearson correlation coefficient Mk；
S26 updates the assumed characteristic impedance value using the following equation:
Z0·k+1＝Z0·k+λ (11)
in the formula, λ is a step length.
S27 repeating the steps S22 to S26 until the updated assumed characteristic impedance Z0·kThe termination condition is satisfied; the termination condition is Z0·kReaching a given threshold;
s28 records all assumed characteristic impedances Z0·kLower mkAnd the corresponding assumed characteristic impedance is taken as the estimated characteristic impedance Z0。
In step S3, the obtained rho is used1、Z0The variable series impedance Z can be obtained according to the formula (5)s。
In step S4, the input impedance Z of the cable head end can be obtained according to the formula (3)in。
Further, step S5 is included for dividing p1、Z0The reflection coefficient gamma under the condition of head end impedance matching can be obtained by substituting the formula (10)1(ω) as shown by the following formula:
Figure BDA0003456783040000051
according to the obtained rho1、Z0The reflection coefficient Γ in the case of head end impedance matching can be obtained according to equation (12)1(ω)。
After the impedance matching processing of the head end is carried out, the head end reflection is greatly compensated, so that the positioning peak value is very close to the actual value.
For cables with impedance mismatch locations, the frequency domain representation U of the reflected signal after impedance matching processing at the head end is eliminated when the reflection at the tail end of the cable is not considered2(ω) can be represented by the following formula:
Figure BDA0003456783040000052
the real part of the reflection coefficient gamma (omega) can be obtained through Euler's formula and traveling wave theoryrealAs shown below (neglecting attenuation):
Figure BDA0003456783040000053
wherein v is the cable phase velocity; v. of1The phase velocity is the area of the cable impedance mismatch location.
Based on the analysis, the invention further provides a cable intermediate joint reflection state evaluation method based on head end impedance matching, and a trigonometric function superposition method is adopted to realize effective judgment of the reflection type and the reflection polarity of the cable impedance mismatching position (comprising the intermediate joint and the transition resistor). The method comprises the following specific steps:
l1 measures the reflection coefficient gamma of the head end of the cable based on the FDR positioning method0(ω) and obtaining the impedance mismatch location in the cable under test;
l2 pair measured reflection coefficient gamma of the head end of the cable0(omega) performing head end impedance matching to obtain a reflection coefficient gamma under the condition of head end impedance matching1(ω)；
L3 extracting gamma1(ω) and obtaining an FDR localization map, recording the signal intensity A of the impedance mismatch location in step L10；
L4 uses ω as argument to construct cosine function g (ω) corresponding to the impedance mismatch position in step L1, and the amplitude of g (ω) is taken as signal intensity A corresponding to the position in step L30；
L5 converting gamma1Summing and differencing the real part of (omega) with g (omega);
l6 extracting FDR positioning map of summed and differentiated signal, recording signal intensity of corresponding impedance mismatch position as A1、A2；
L7 if min { A } is satisfied1，A2}≤0.5A0And max { A1，A2}≥1.5A0If the reflection type is recorded as transition resistance, otherwise, the reflection type is recorded as an intermediate joint; wherein min {. cndot, max {. cndot } are minimum and maximum functions, respectively;
l8 if satisfying A1<A2If the reflection polarity is negative at the position corresponding to the impedance mismatching, the mark alpha is-1; otherwise, the reflection polarity is positive, and α is 1.
The existing research results show that the attenuation of the signal is exponential function when the signal propagates in the cable, so that the effective compensation of the attenuation can be realized by using a linear function in a logarithmic coordinate. Therefore, the invention combines the multiple refraction and reflection principle of the traveling wave to set the reflected signal intensity P in the k' th iterationkFirstly, acquiring the signal intensity of each impedance mismatch position under the condition of no attenuation according to the cable terminal intensity; and then determining the reflection coefficient according to the reflection type of each impedance mismatching position and correcting. In particular implementations, the meter may be further acquired using the following stepsCalculating the reflection coefficient of each position when the cable has a plurality of impedance mismatching positions:
l9 records the cable termination reflected signal strength pendAnd use it as Pk′An initial value, k', is the number of iterations;
l10 uses the following equation to calculate the signal strength p at each impedance mismatch location without attenuationi0：
Figure BDA0003456783040000061
In the formula: p is a radical ofiTo locate the signal strength of the ith impedance mismatch location in the map; liDistance corresponding to the impedance mismatch location;
l11 jumping to step L12 when the impedance mismatch position is the middle joint, otherwise, recording the reflection coefficient as rhoi＝αpi0And jumps to step L13;
l12 constructs a cosine function signal g shown in formula (14)i(ω), then g is obtainedi(omega) corresponding position signal intensity and p in positioning mapi0Closest xiAnd recording the reflection coefficient as rhoi＝αxiThen proceed to step L13;
l13 corrects each reflection coefficient of the impedance mismatch location as follows:
Figure BDA0003456783040000062
in the formula: j is an index point of the set transition resistance;
l14 reflected signal strength based on the corrected impedance mismatch location is given by PkUpdating:
Figure BDA0003456783040000063
where i is 1,2, …, N represents the total number of impedance mismatch locations.
L15 repeats steps L10 to L14 until the termination condition is satisfied; the termination condition is that an upper limit of the iteration number is reached. Finally, the result of the correction by L13 is used as the reflection coefficient of each impedance mismatch position of the cable.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention provides a head end impedance matching method, which is realized by introducing a variable resistor ZsEffectively calculating the reflection coefficient of the head end of the cable and the characteristic impedance of the cable to obtain the input impedance Z of the head end of the cableinTherefore, effective correction of field FDR data is achieved, and the influence of impedance mismatching of the head end caused by stray parameters of the branched lead on a test result is restrained; and the reflection coefficient under the condition of impedance matching of the head end of the cable can be further obtained.
2. On the basis of realizing the impedance matching of the head end, the invention can further realize the effective judgment of the reflection type and the reflection polarity of the impedance mismatching position of the cable, and can further obtain the reflection coefficient of the impedance mismatching position of the cable, thereby providing guiding significance for the practical application of the FDR in the field.
Drawings
FIG. 1 is a schematic diagram of an impedance mismatch reflection coefficient model according to the present invention;
FIG. 2 is a schematic diagram of the FDR test principle according to the present invention;
FIG. 3 is a schematic diagram illustrating the effect of stray parameters on a bifurcated lead according to the present invention;
FIG. 4 is a schematic diagram of modeling at a bifurcated lead in accordance with the present invention;
FIG. 5 is a schematic diagram of the results of the head end impedance matching process of the present invention;
FIG. 6 is a schematic view of the results of the intermediate joint process of the present invention;
FIG. 7 is a schematic view of a reflection coefficient testing platform for a cable according to the present invention;
FIG. 8 is a schematic diagram of the test and positioning results of the 1# impedance mismatch location of the present invention;
FIG. 9 is a schematic diagram of the 2# impedance mismatch location test and positioning results of the present invention;
FIG. 10 is a graph showing the results of the reflection coefficient test of the 500m power cable according to the present invention;
FIG. 11 is a schematic view of a 500m power cable intermediate connector positioning map according to the present invention;
FIG. 12 is a TDR test result of 500m power cable according to the present invention.
Detailed Description
The technical solutions of the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings, and it is to be understood that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, belong to the present invention.
The FDR positioning spectrogram acquisition method used in the following examples employs a conventional method in the art, specifically referred to impedance change type determination technology [ J ] in the frequency domain reflectometry of rocain county jey, trivia, huang-yonghu, lismingzo, lish, 2021,36 (16): 3457-3466.
Pearson's correlation coefficient m in the following exampleskThe methods for obtaining (a) are conventional in the art.
Example 1
The principle of the FDR test on which this example is based is shown in Table 2.
The head end impedance matching method suitable for the FDR test provided by the embodiment includes the following steps:
s1 takes Gaussian pulse as incident signal, FDR test is carried out on the cable connected with the branch lead to obtain the reflection coefficient gamma of the head end of the cable0(omega), then acquiring frequency domain reflection signals according to the reflection coefficients and the Gaussian pulse signals respectively; then according to the first reflection pulse signal and the Gaussian pulse signal obtained by the frequency domain reflection signal, obtaining the reflection coefficient rho of the head end of the cable1。
In this step, a Gaussian pulse is introduced as an incident signal, and then a reflection coefficient gamma is used0(omega) calculating to obtain a time domain reflection signal, and finally extracting a first reflection pulse to realize rho1Obtaining the target value. Comprises the following steps：
S11 measuring reflected signal U from head end by tester with Gaussian pulse as incident signal1(omega) with the incident signal U0(omega) ratio to obtain reflection coefficient gamma of head end of cable0(ω), i.e.
Figure BDA0003456783040000081
S12 generating the Gaussian pulse signal y using the following formula0(t)：
Figure BDA0003456783040000082
In the formula, w is a gaussian pulse width, and the value in this embodiment is the reciprocal of the upper limit value of the scanning frequency of the vector network analyzer; t is time;
s13 pairs of Gaussian pulse signals y0(t) performing Fast Fourier Transform (FFT) processing to obtain Y0(ω), i.e. Y0(ω)＝FFT(y0(t))。
S14, calculating to obtain the frequency domain expression Y of the reflected signal by using the following formula1(ω)：
Y1(ω)＝Y0(ω)·Γ0(ω) (8)
S15 pair of reflected signals Y1(omega) performing Inverse Fast Fourier Transform (IFFT) processing to obtain y1(t), i.e. y1(t)＝IFFT(Y1(ω))。
S16 intercepting y by time window1(t) first reflection pulse y2(t), the first peak measured in the time domain.
S17 for the first reflected pulse y2(t) FFT processing to obtain Y2(ω), i.e. Y2(ω)＝FFT(y2(t))；
S18 is calculated by the following formula1：
Figure BDA0003456783040000083
S2 obtaining the characteristic impedance Z of the cable by adopting an enumeration method0。
In this step, the characteristic impedance Z is assumed first0·kAnd endowing the initial value with a random value, determining variable series impedance and head end input impedance, and then iteratively updating the assumed characteristic impedance until the assumed characteristic impedance meets the termination condition.
In a specific implementation manner, the step includes the following sub-steps:
s21 pairs of hypothetical characteristic impedances Z0·kIs assigned, where the value is 10 omega, k represents the number of cycles,
initially k is 1;
s22 variable series impedance Z under the assumed characteristic impedance is calculated by formula (5)sNamely:
Figure BDA0003456783040000091
s23 the reflection coefficient gamma under the condition of head end impedance matching is calculated by the formula (10)1(omega) and head end input impedance Zin(ω), i.e.:
Figure BDA0003456783040000092
s24 for ZinThe phase of (ω) is FFT processed, only the data at the cable termination position is retained, and other data is zeroed and IFFT processed.
In this step, due to ZinThe phase position of (omega) is the inverse tangent value of the ratio of the imaginary part to the real part, so that the frequency of the phase position after FFT transformation is unchanged, the frequency corresponding to the cable terminal position is found out according to the FDR positioning spectrogram obtaining method, other frequencies are set to be 0, and after IFFT processing is carried out, the input impedance only containing the cable terminal is obtained.
S25 comparing the first M cycles of the data obtained by IFFT processing in step S24 with Z cycles in step S23inComparing the first M periods of the (omega) phase and obtaining the Pearson correlation coefficientmkIn this embodiment, M is 5.
S26 updates the assumed characteristic impedance value using the following equation:
Z0·k+1＝Z0·k+λ (11)
in the formula, λ is a step length, and the value in this embodiment is 0.1 Ω.
S27 repeating the steps S22 to S26 until the updated assumed characteristic impedance Z0·kThe termination condition is satisfied; the termination condition is Z0·kReach a given threshold, in this example Z0·kThe termination number is 100 Ω;
s28 records all assumed characteristic impedances Z0·kLower mkAnd the corresponding assumed characteristic impedance is taken as the estimated characteristic impedance Z0。
S3 reflection coefficient rho according to head end of cable1Characteristic impedance Z of cable0Obtaining a variable series impedance Z according to equation (5)s：
Figure BDA0003456783040000093
S4 based on variable series impedance ZsCalculating the input impedance Z of the head end of the cable according to the formula (3)in：
Figure BDA0003456783040000101
The head end impedance matching in the FDR test can be realized according to the steps S1-S4.
Example 2
This example is an improvement on example 1.
The head end impedance matching method suitable for FDR test provided in this embodiment further includes step S5, where the obtained ρ is obtained1、Z0The reflection coefficient gamma under the condition of head end impedance matching can be obtained by substituting the formula (10)1(ω) as shown by the following formula:
Figure BDA0003456783040000102
example 3
The embodiment is a further improvement on the embodiment 2.
The embodiment provides a cable intermediate joint reflection state evaluation method based on head end impedance matching, and a trigonometric function superposition method is adopted to effectively judge the reflection type and the reflection polarity of a cable impedance mismatching position (comprising an intermediate joint and a transition resistor). The method comprises the following specific steps:
l1 measures the reflection coefficient gamma of the head end of the cable based on the FDR positioning method0And (omega) and acquiring the impedance mismatch position in the tested cable.
L2 pair measured reflection coefficient gamma of the head end of the cable0(ω) the head-end impedance matching was performed by the method described in example 2 to obtain the reflection coefficient Γ in the case of head-end impedance matching1(ω)。
L3 extracting gamma1(ω) and obtaining an FDR localization map, recording the signal intensity A of the impedance mismatch location in step L10；
L4 constructs a cosine function g (omega) of the corresponding impedance mismatch position in the step L1 by using omega as an independent variable according to the following formula, wherein the amplitude of the g (omega) is taken as the signal intensity A of the corresponding position in the step L30：
Figure BDA0003456783040000103
Wherein f is the test frequency; v is the cable phase velocity; v. of1The phase velocity is the cable impedance mismatch position area; where ρ is2＝A0；l1Representing the distance from the cable impedance mismatch location to the cable head end, d the length of the impedance mismatch location.
In this embodiment, g (ω) may be represented by Γ (ω)realThe first two items of (1).
L5 using the L2 to obtain gamma1Summing and subtracting the real part of (omega) and g (omega) obtained in the step L4;
l6 extracting FDR positioning map of summed and differenced signals, and recording signal intensity A of corresponding impedance mismatch position1、A2；
L7 if min { A } is satisfied1，A2}≤0.5A0And max { A1，A2}≥1.5A0If the reflection type is recorded as transition resistance, otherwise, the reflection type is recorded as an intermediate joint; wherein min {. cndot, max {. cndot } are minimum and maximum functions, respectively;
l8 if satisfying A1<A2If the reflection polarity is negative at the position corresponding to the impedance mismatching, the mark alpha is-1; otherwise, the reflection polarity is positive, and α is 1.
Example 4
The embodiment is a further improvement on the embodiment 3.
The embodiment of the invention combines the multiple refraction and reflection principle of the traveling wave and sets the (reflected signal strength in the k' th iteration) Pk′Firstly, acquiring the signal intensity of each impedance mismatch position under the condition of no attenuation according to the cable terminal intensity; and then determining the reflection coefficient according to the reflection type of each impedance mismatching position and correcting. In a specific implementation manner, the reflection coefficient of each position of the cable at the presence of a plurality of impedance mismatch positions can be further obtained and calculated by the following steps:
l9 records the cable termination reflection intensity pendAnd use it as Pk′An initial value.
In this step, the cable terminal reflection intensity p in the FDR positioning map of the head end reflection coefficient obtained by the processing of the head end impedance matching methodendAs Pk′An initial value. (ii) a
L10 uses the following equation to calculate the signal strength p at each impedance mismatch location without attenuationi0：
Figure BDA0003456783040000111
In the formula：piSignal strength at the ith impedance mismatch location in the FDR localization map for the head end reflection coefficient obtained in step L9; liDistance corresponding to the impedance mismatch location; for convenience of analysis, the impedance mismatch positions are sorted in the order of the distances from small to large in this embodiment.
L11 jumping to step L12 when the impedance mismatch position is the middle joint, otherwise, recording the reflection coefficient as rhoi＝αpi0And jumps to step L13.
L12 constructs a cosine function signal g shown in formula (14)i(ω), then g is obtainedi(omega) corresponding position signal intensity and p in positioning mapi0Closest xiAnd recording the reflection coefficient as rhoi＝αxiThen, the process proceeds to step L13.
In this step, the cosine function g of the ith impedance mismatch location is constructed as given in L4 abovei(ω), here the first 2 terms are taken, the amplitudes are respectively
Figure BDA0003456783040000112
Then obtain gi(ω) FDR localization Profile, then Signal Strength and p from the ith impedance mismatch locationi0Equality, calculating to obtain corresponding xi. Then according to rhoi＝αxiAnd obtaining the reflection coefficient of the impedance mismatch position.
L13 corrects each reflection coefficient of the impedance mismatch location as follows:
Figure BDA0003456783040000121
in the formula: j is the index point of the set transition resistance.
L14 reflected signal strength P based on corrected impedance mismatch positionk′The update is performed as follows:
Figure BDA0003456783040000122
where i is 1,2, …, N represents the total number of impedance mismatch locations.
L15 repeats steps L10 to L14 until the termination condition is satisfied; the termination condition is that the upper limit of the iteration number is reached, in this embodiment, the termination condition is that the iteration number reaches 10 times, that is, the upper limit of the iteration number is 10 times.
Application example 1
In this application, a lossless cable model is used as a research object, and the method provided in the foregoing embodiment 2 is used to perform head-end impedance matching processing, so as to obtain an FDR positioning spectrogram of a first-segment reflection coefficient, as shown in fig. 5.
As can be seen from fig. 5, the value of the positioning peak (cable termination) without the head end impedance matching process is significantly lower than the actual value due to the influence of the stray parameters of the branched leads, which will also have an influence on the accurate evaluation of the reflection intensity thereof. After the impedance matching processing of the head end is carried out, the head end reflection is greatly compensated, so that the positioning peak value is very close to the actual value.
Application example 2
In order to verify the effectiveness of the reflection type and reflection polarity judging method, the application example utilizes MATLAB to construct YJLV8.7/15-3 × 95 cable with the length of 500m, the simulation frequency is set to be 0.3-10 MHz, and the number of frequency sweeping points is set to be 1000. The cable middle tap capacitance was set to 0.848 times the bulk capacitance and the middle tap length was set to 0.8m (positive polarity). The impedance mismatch location (here the intermediate junction) is set to 300 m.
Fig. 6 and table 1 show the results of the determination according to the method for estimating the reflection state of the cable intermediate joint based on the head end impedance matching provided in the foregoing embodiment 3.
TABLE 1 determination of reflection type and reflection polarity
Figure BDA0003456783040000123
As can be seen from fig. 6 and the results in table 1, in the cable intermediate joint, since the reflection is a superposition of a plurality of reflections, the intensity change of the signal after the superposition summation and the subtraction is not obvious, but the reflection polarity can be effectively determined according to the relative magnitude. Therefore, the superposition method provided by the invention can effectively judge the reflection type and the reflection polarity.
Application example 3
In order to verify the effectiveness of the method provided by the invention in practical tests, the application example firstly builds an experimental platform shown in fig. 7. In the present application, coaxial cable RG142 was used as a study target, and coaxial cable RG142 to be measured had a length of 39.6m and a characteristic impedance of 50 Ω (Z)0) The dummy linker portion used was 0.4m (d) in length and 75. omega. in characteristic impedance (Z)1) The RG179 coaxial cable was simulated with the simulated joints set at 9.6m (1#) and 29.6m (2#), respectively (for both conditions). In order to keep consistent with the actual testing mode on site, the testing head end adopts a branch line to carry out testing (mismatching). The reflection coefficient test result and the positioning map (effective data is selected to be 0.3-50 MHz) obtained by performing the test in the range of 0.3-100 MHz by using VNA 3E are respectively shown as gray solid lines in FIG. 8 and FIG. 9.
The reflection coefficient obtained by the test is processed by using the head-end impedance matching technology provided in embodiment 1, and the characteristic impedances of the cables estimated under the two working conditions are 52.1 Ω and 52.0 Ω, respectively. The real part of the reflection coefficient and the mapping map obtained after the treatment according to example 2 are shown as black solid lines in fig. 8 and 9, respectively. As can be seen from fig. 8 and 9, after the head-end impedance matching processing, the degree of distortion of the reflection coefficient is smaller, multiple reflections caused by the mismatch of the head ends of the cables in the positioning map are also significantly reduced, and the signal strength of the cable intermediate connector and the cable terminal is significantly enhanced.
The results obtained by using the reflection type and the reflection polarity determination provided in example 3 and the reflection coefficient approximation calculation method provided in example 4 are shown in tables 2 and 3, respectively.
TABLE 2 reflection type and polarity of reflection for two analog connectors
Figure BDA0003456783040000131
TABLE 3 reflection coefficients of two simulated joints
Figure BDA0003456783040000132
As can be seen from the results of tables 2 and 3, the method provided by the present invention can effectively identify the impedance mismatch position and determine the polarity thereof, and the error between the calculated reflection coefficient and the actual value is small.
Application example 4
Further, in order to verify the effectiveness of the method in evaluating the reflection state of the power cable, a test instrument and a test method shown in fig. 7 are used to test a ZC-YJLV 228.7/153 × 95 power cable (with an intermediate joint located 250m from the head end of the power cable) with a length of 500m within a range of 0.3 to 15MHz, and then the reflection coefficient test result and the positioning map (effective data is selected to be 0.3 to 7MHz) obtained according to example 2 under the condition of matching the head end are respectively shown in fig. 10 and 11.
As can be seen from fig. 10 and 11, the head end reflection distortion is effectively suppressed after the head end impedance matching, and the intermediate connector position and the terminal position signal in the positioning map are enhanced. It should also be noted that when the cable head end is mismatched, the multiple reflection signal strength is suppressed in fig. 11 after head end impedance matching because the mid-tap location (250m) produces two reflections (head end and terminal) at the 750m location.
Using the calculation methods described in examples 1-4, the characteristic impedance (Z) of the power cable to be measured is obtained0) Is 37.7 omega, A0＝0.021，A1＝0.031，A2When the reflection polarity is positive, the reflection coefficient is 0.212 (0.027). In order to verify the accuracy of the determination result, the TDR cable fault locator is used to test the power cable, and the test result is shown in fig. 12. As can be seen from fig. 12, the reflected wave at the position of the middle joint in the TDR test result is a positive-negative superimposed waveform, and is consistent with the determination result of the present application example.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (9)

1. A head end impedance matching method suitable for FDR testing, comprising the steps of:
s1 takes Gaussian pulse as incident signal, FDR test is carried out on the cable connected with the branch lead to obtain the reflection coefficient gamma of the head end of the cable0(omega), then acquiring frequency domain reflection signals according to the reflection coefficients and the Gaussian pulse signals respectively; then obtaining a reflection coefficient rho of the head end of the cable according to a first reflection pulse signal and a Gaussian pulse signal obtained by frequency domain reflection signals1；
S2 obtaining the characteristic impedance Z of the cable by adopting an enumeration method0；
S3 reflection coefficient rho according to head end of cable1Characteristic impedance Z of cable0The variable series impedance Z is obtained according to the following formulas：
Figure FDA0003456783030000011
In the formula, R0Is the characteristic impedance of the coaxial cable connected between the tester and the cable;
s4 based on variable series impedance ZsCalculating the input impedance Z of the head end of the cable according to the following formulain：
Figure FDA0003456783030000012
In formula (II), Z'inAnd (omega) is the input impedance of the head end of the cable measured by the tester.
2. The method as claimed in claim 1, wherein the step S1 comprises the following sub-steps:
s11 using Gaussian pulse as incident signal, measuring the ratio of the reflected signal and incident signal at the head end by the tester to obtain the reflection coefficient gamma of the head end of the cable0(ω)；
S12 generating the Gaussian pulse signal y using the following formula0(t)：
Figure FDA0003456783030000013
In the formula, w is the Gaussian pulse width; t is time;
s13 pairs of Gaussian pulse signals y0(t) performing Fast Fourier Transform (FFT) to obtain Y0(ω)；
S14, calculating to obtain the frequency domain expression Y of the reflected signal by using the following formula1(ω)：
Y1(ω)＝Y0(ω)·Γ0(ω)
S15 pair of reflected signals Y1(omega) carrying out Inverse Fast Fourier Transform (IFFT) processing to obtain y1(t)；
S16 intercepting y by time window1(t) first reflection pulse y2(t)；
S17 for the first reflected pulse y2(t) FFT processing to obtain Y2(ω)；
S18 is calculated by the following formula1：
Figure FDA0003456783030000014
3. The method of matching a head end impedance for FDR testing as claimed in claim 1 or 2, wherein step S2 comprises the sub-steps of:
s21 gives an assumed characteristic impedance, and gives an assumed characteristic impedance Z0·kAssigning the initial value of (a), wherein k represents the cycle number;
s22 the variable series impedance Z under the assumed characteristic impedance is calculated by the following formulas；
Figure FDA0003456783030000021
S23 calculating the input impedance Z under the condition of head end impedance matching by using the following formulain(ω)：
Figure FDA0003456783030000022
Z′in(omega) is the input impedance of the head end of the cable measured by the tester;
s24 for ZinPerforming FFT processing on the phase of (omega), only retaining data of the cable terminal position, and performing IFFT processing on other data by setting zero;
s25 comparing the first M cycles and Z of the data obtained by IFFT processing in step S24inComparing the first M periods of the (omega) phase and obtaining the Pearson correlation coefficient Mk；
S26 updates the assumed characteristic impedance value using the following equation:
Z0·k+1＝Z0·k+λ
in the formula, lambda is the step length;
s27 repeating the steps S22 to S26 until the updated assumed characteristic impedance Z0·kThe termination condition is satisfied; the termination condition is Z0·kReaching a given threshold;
s28 records all assumed characteristic impedances Z0·kLower mkAnd the corresponding assumed characteristic impedance is taken as the estimated characteristic impedance Z0。
4. The method for matching impedance of a head end suitable for FDR testing as recited in claim 1 or 2, further comprising a step S5 of obtaining ρ1、Z0The head end resistance is obtained according to the following formulaReflection coefficient Γ in the case of anti-matching1(ω)：
Figure FDA0003456783030000023
5. A cable intermediate joint reflection state evaluation method based on head end impedance matching is characterized in that effective judgment of reflection types and reflection polarities of impedance mismatching positions is achieved by a trigonometric function superposition method.
6. The method for estimating the reflection state of the intermediate joint of the cable based on the impedance matching at the head end as claimed in claim 5, wherein the method comprises the following steps:
l1 measures the reflection coefficient gamma of the head end of the cable based on the FDR positioning method0(ω) and obtaining the impedance mismatch location in the cable under test;
l2 pair measured reflection coefficient gamma of the head end of the cable0(ω) obtaining the reflection coefficient Γ in the case of head-end impedance matching by performing the head-end impedance matching processing according to the head-end impedance matching method of claim 41(ω)；
L3 extracting gamma1(ω) and obtaining an FDR localization map, recording the signal intensity A of the impedance mismatch location in step L10；
L4 uses ω as argument to construct cosine function g (ω) corresponding to the impedance mismatch position in step L1, and the amplitude of g (ω) is taken as signal intensity A corresponding to the position in step L30；
L5 converting gamma1Summing and differencing the real part of (omega) with g (omega);
l6 extracting FDR positioning map of summed and differentiated signal, recording signal intensity of corresponding impedance mismatch position as A1、A2；
L7 if min { A } is satisfied1，A2}≤0.5A0And max { A1，A2}≥1.5A0If the reflection type is recorded as transition resistance, otherwise, the reflection type is recorded as an intermediate joint; wherein min { · },max {. is a function of the minimum value and the maximum value respectively;
l8 if satisfying A1<A2If the reflection polarity is negative at the position corresponding to the impedance mismatching, the mark alpha is-1; otherwise, the reflection polarity is positive, and α is 1.
7. The head-end impedance matching-based cable intermediate joint reflection state evaluation method as claimed in claim 6, wherein in step L4, Γ (ω) is intangibly according to the following formularealStructure g (ω):
Figure FDA0003456783030000031
wherein f is the test frequency; v is the cable phase velocity; v. of1The phase velocity is the cable impedance mismatch position area; rho2＝A0；l1Representing the distance from the cable impedance mismatch location to the cable head end, d the length of the impedance mismatch location.
8. The method for estimating the reflection state of the intermediate joint of the cable based on the impedance matching at the head end as claimed in claim 5, 6 or 7, wherein the signal strength of each impedance mismatch position under the condition of no attenuation is further obtained according to the cable termination strength; and then determining the reflection coefficient according to the reflection type of each impedance mismatching position and correcting.
9. The method for estimating the reflection state of a cable intermediate joint based on head-end impedance matching as claimed in claim 8, wherein in a specific implementation, the reflection coefficient of each position of the cable at which a plurality of impedance mismatch positions exist is further obtained by using the following steps:
l9 records the cable termination reflection intensity pendAnd use it as PkAn initial value;
l10 uses the following equation to calculate the signal strength p at each impedance mismatch location without attenuationi0：
Figure FDA0003456783030000041
In the formula: p is a radical ofiTo locate the signal strength of the ith impedance mismatch location in the map; liDistance corresponding to the impedance mismatch location;
l11 jumping to step L12 when the impedance mismatch position is the middle joint, otherwise, recording the reflection coefficient as rhoi＝αpi0And jumps to step L13;
l12 constructs cosine function signal gi(ω), then g is obtainedi(omega) corresponding position signal intensity and p in positioning mapi0Closest xiAnd recording the reflection coefficient as rhoi＝αxiThen proceed to step L13;
l13 corrects each reflection coefficient of the impedance mismatch location as follows:
Figure FDA0003456783030000042
in the formula: j is an index point of the set transition resistance;
l14 reflection coefficient based on corrected impedance mismatch position as given by PkUpdating:
Figure FDA0003456783030000043
wherein i is 1,2, …, N represents the total number of impedance mismatch locations;
l15 repeats steps L10 to L14 until the termination condition is satisfied.
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