CN114492284A - High-voltage cable joint frequency response modeling method considering broadband characteristic of semi-conductive shielding layer - Google Patents

High-voltage cable joint frequency response modeling method considering broadband characteristic of semi-conductive shielding layer Download PDF

Info

Publication number
CN114492284A
CN114492284A CN202111516218.9A CN202111516218A CN114492284A CN 114492284 A CN114492284 A CN 114492284A CN 202111516218 A CN202111516218 A CN 202111516218A CN 114492284 A CN114492284 A CN 114492284A
Authority
CN
China
Prior art keywords
cable joint
unit circuit
frequency
shielding layer
unit
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202111516218.9A
Other languages
Chinese (zh)
Inventor
侯帅
惠宝军
傅明利
黎小林
朱闻博
展云鹏
冯宾
张逸凡
章彬
伍国兴
徐曙
陈潇
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
CSG Electric Power Research Institute
Shenzhen Power Supply Bureau Co Ltd
Original Assignee
CSG Electric Power Research Institute
Shenzhen Power Supply Bureau Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by CSG Electric Power Research Institute, Shenzhen Power Supply Bureau Co Ltd filed Critical CSG Electric Power Research Institute
Priority to CN202111516218.9A priority Critical patent/CN114492284A/en
Publication of CN114492284A publication Critical patent/CN114492284A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/39—Circuit design at the physical level
    • G06F30/392—Floor-planning or layout, e.g. partitioning or placement
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/39—Circuit design at the physical level
    • G06F30/398—Design verification or optimisation, e.g. using design rule check [DRC], layout versus schematics [LVS] or finite element methods [FEM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/16—Cables, cable trees or wire harnesses

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Architecture (AREA)
  • Insulated Conductors (AREA)

Abstract

The invention provides a high-voltage cable joint frequency response modeling method considering the broadband characteristic of a semi-conductive shielding layer, which comprises the steps of measuring the complex dielectric constant of the inner semi-conductive shielding layer and the outer semi-conductive shielding layer of a cable joint in a preset frequency range, and fitting the complex dielectric constant along with the frequency change relation to obtain the complex dielectric constant equation of the inner semi-conductive shielding layer and the outer semi-conductive shielding layer of the cable joint; performing segmentation equivalent processing on the cable joint according to the difference of the internal structure of the cable joint, and establishing a distribution parameter equivalent circuit considering the conductor crimping of the cable joint according to a segmentation result; and calculating frequency domain response characteristic parameters of the cable joint through a complex dielectric constant equation, wherein the frequency domain response characteristic parameters comprise characteristic impedance, wave velocity and propagation coefficient, a transfer matrix and a transmission coefficient, so that the propagation characteristics of different central frequency signals at the cable joint and the frequency dependence characteristics of the cable joint can be analyzed according to the frequency domain response characteristic parameters.

Description

High-voltage cable joint frequency response modeling method considering broadband characteristic of semi-conductive shielding layer
Technical Field
The invention relates to the technical field of high voltage and insulation, in particular to a high-voltage cable joint frequency response modeling method considering the broadband characteristic of a semiconductive shielding layer.
Background
With the rapid development of domestic ultra-large cities, the number of power cables in urban power grids rapidly increases due to excellent electrical properties. The good and stable normal operation of dense power cables in cities is directly related to the safety and reliability of urban power grids.
Under the condition that a cable normally runs and is often invaded by transient overvoltage, Fourier spectrum analysis is carried out on different types of overvoltage, the main frequency band of operation waves is distributed in a range of a plurality of kHz, the transient component of lightning waves is concentrated below 1MHz, and the main frequency band of very fast transient overvoltage VFTO is distributed in a range of a plurality of MHz to a plurality of dozens of MHz. And under the condition of cable fault, a fault point needs to be positioned by utilizing a sweep frequency signal, and the stop frequency of an incident signal is as high as 100 MHz. It can be seen that the cable is subject to the intrusion of waves from several kHz to hundreds of MHz under different operating conditions, which adds complexity to the evaluation of the operation of the cable.
The cable joint is used as the weakness of a cable system, and has important significance for the research of broadband response characteristics in different frequency ranges. Research has proved that the inner and outer semiconductive shielding layers of the cable joint have strong frequency dependence and have significant influence on the wave propagation process. However, the frequency variation characteristics of the inner and outer semiconductive shielding layers are not considered in the prior art, so that the frequency variation characteristics of the frequency response characteristics of the cable joint cannot be accurately described.
Disclosure of Invention
The invention provides a high-voltage cable joint frequency response modeling method considering the broadband characteristic of a semi-conductive shielding layer, which can analyze the frequency response characteristic of a cable joint by considering the frequency variation characteristics of an inner semi-conductive shielding layer and an outer semi-conductive shielding layer of the cable joint.
The invention provides a high-voltage cable joint frequency response modeling method considering broadband characteristics of a semiconductive shielding layer, which comprises the following steps of:
obtaining a first complex dielectric constant and a second complex dielectric constant which are obtained by measuring the preprocessed sample of the inner semi-conductive shielding layer and the preprocessed sample of the outer semi-conductive shielding layer in a preset frequency range;
respectively fitting the variation relation of the first complex dielectric constant and the second complex dielectric constant along with the frequency to obtain a first complex dielectric constant equation corresponding to the inner semi-conductive shielding layer sample and a second complex dielectric constant equation corresponding to the outer semi-conductive shielding layer sample;
performing segmentation equivalent processing on the cable joint according to the difference of the internal structure of the cable joint, and establishing a distribution parameter equivalent circuit considering the conductor crimping of the cable joint according to a segmentation result; wherein the distributed parameter equivalent circuit comprises a plurality of unit circuits;
calculating the impedance and admittance of each unit circuit along with the change of frequency by considering the structure and material characteristics of each unit after segmentation and combining the first complex dielectric constant equation and the second complex dielectric constant equation;
and calculating the characteristic impedance, wave velocity and propagation coefficient of the cable joint along the axial length under different frequencies according to the impedance and admittance of each unit circuit along with the frequency change, and calculating the transfer matrix and the transmission coefficient of the cable joint according to the characteristic impedance and the propagation coefficient.
As an improvement of the above scheme, the performing a segmentation equivalent process on the cable connector according to the difference of the internal structure of the cable connector, and establishing a distribution parameter equivalent circuit considering the crimping of the conductor of the cable connector according to the segmentation result specifically includes:
dividing a left half shaft part of the cable joint into a plurality of units which are connected in series according to the internal structure difference of the cable joint and the axial symmetry characteristic of the cable joint; if the unit is a cable joint non-crimping section, the unit is a first unit; if the unit is the cable joint crimping section, the unit is a second unit;
and establishing each first unit circuit corresponding to each first unit and a second unit circuit corresponding to the second unit so as to establish a distributed parameter equivalent circuit considering the crimping of the cable joint conductor.
As an improvement of the above solution, the calculating impedance and admittance of each unit circuit with frequency change by considering the structure and material characteristics of each unit after segmentation and combining the first complex permittivity equation and the second complex permittivity equation specifically includes:
for each unit circuit, calculating the distribution resistance and the distribution inductance distribution of the unit circuit along with the frequency change, and calculating the impedance of the unit circuit along with the frequency change according to the distribution resistance and the distribution inductance;
calculating the admittance of each material structure layer in the unit circuit along with the change of the frequency, and performing parallel calculation on the admittances of all the material structure layers along with the change of the frequency to obtain the admittance of the unit circuit along with the change of the frequency; the unit circuit comprises a material structure layer, an inner semi-conductive shielding layer and an outer semi-conductive shielding layer, wherein the material structure layer comprises a main insulating layer and a semi-conductive waterproof layer, and at least one of the inner semi-conductive shielding layer and the outer semi-conductive shielding layer, the admittance of the inner semi-conductive shielding layer changing along with the frequency is obtained by calculation according to the first complex dielectric constant equation, and the admittance of the outer semi-conductive shielding layer changing along with the frequency is obtained by calculation according to the second complex dielectric constant equation.
As an improvement of the above scheme, the distributed resistance of the unit circuit with frequency variation is calculated by the following steps:
when the unit circuit is a first unit circuit, calculating the distributed resistance of the first unit circuit along with the frequency change according to the following formula:
Figure RE-GDA0003557725920000031
when the unit circuit is a second unit circuit, calculating the distributed resistance of the second unit circuit along with the frequency change according to the following formula:
Figure RE-GDA0003557725920000032
Figure RE-GDA0003557725920000033
a′＝a″+Δd
Figure RE-GDA0003557725920000034
wherein R (ω) is the distributed resistance of the first unit, ω is the angular frequency, a1Is the outer radius of the inner conductor, a2Is the inner radius of the outer conductor, p1Is the resistivity of the inner conductor, p2Is the resistivity of the outer conductor, mu0For the vacuum permeability, R ' (ω) is the distributed resistance of the second unit, K is the contact coefficient, a ' is the radius of the conductor of the cable body, a ' is the radius of the conductor of the crimp section of the cable joint, ρ ' is the normal conductor resistivity, ρ ' cableAnd the conductor resistivity of the joint crimping section, deltad is the thickness of the cable joint crimping section, l is the length of the first unit circuit, and l' is the length of the second unit circuit.
As an improvement of the above solution, the distributed inductance of the unit circuit is obtained by:
when the unit circuit is a first unit circuit, calculating the distributed inductance of the first unit circuit according to the following formula:
Figure RE-GDA0003557725920000041
when the unit circuit is a second unit circuit, calculating the distributed inductance of the second unit circuit according to the following formula:
Figure RE-GDA0003557725920000042
Figure RE-GDA0003557725920000043
Figure RE-GDA0003557725920000044
wherein L (ω) is the distributed inductance of the first unit circuit, ω is the angular frequency, a1Is the radius of the conductor of the cable body, a2Inner radius of the outer conductor, mu0For vacuum permeability, p1Resistivity of the inner conductor, p2In terms of the resistivity of the outer conductor, L '(ω) is the distributed inductance of the second unit, ρ ″ the conductor resistivity of the cable joint crimping section, a ″ is the radius of the conductor of the cable joint crimping section, Y is the axial length of the cable joint crimping section, L is the length of the first unit circuit, and L' is the length of the second unit circuit.
As an improvement of the above scheme, the admittance of the inner semiconductive shielding layer with respect to the frequency is calculated according to the first complex permittivity equation, and the admittance of the outer semiconductive shielding layer with respect to the frequency is calculated according to the second complex permittivity equation, specifically:
the admittance of the inner semiconductive shield layer is calculated according to the following equation:
Figure RE-GDA0003557725920000051
the admittance of the outer semiconductive shield is calculated according to the following equation:
Figure RE-GDA0003557725920000052
wherein, Y1(omega) is the admittance of the inner semiconducting shield layer, omega is the angular frequency, epsilon0In order to have a dielectric constant in a vacuum,
Figure RE-GDA0003557725920000053
is a first complex permittivity equation, ro1Is the outer radius of the inner semiconductive shield layer, ri1Is the inner radius of the inner semiconductive shield layer, Y2(ω) is the admittance of the outer semiconductive shield layer,
Figure RE-GDA0003557725920000054
is a second complex permittivity equation, ro2Is the outer radius of the outer semiconductive shield layer, ri2The inner radius of the outer semiconductive shield layer.
As an improvement of the above scheme, the transfer matrix of the cable joint is calculated by the following steps:
the cable joint is equivalent to a plurality of units which are coaxially connected in series, and the transfer matrix characteristic parameters of each unit are calculated according to the propagation coefficient, the axial length and the characteristic impedance corresponding to each unit;
and calculating the product of the transfer matrix characteristic parameters of all the units to obtain the transfer matrix of the cable joint.
As an improvement of the above scheme, the transfer matrix characteristic parameter of the cell is calculated by the following formula:
Figure RE-GDA0003557725920000055
wherein the content of the first and second substances,
Figure RE-GDA0003557725920000056
characteristic parameter of transfer matrix, gamma, representing the ith celliIs the propagation coefficient corresponding to the ith unit circuit in the equivalent circuit, liIs the axial length of the i-th cell, ZoiThe characteristic impedance corresponding to the ith unit circuit in the equivalent circuit.
As an improvement of the above solution, the transmission coefficient of the cable joint is calculated by the following formula:
Figure RE-GDA0003557725920000057
wherein, TjIs the transmission coefficient of the cable joint, ZoA, B, C, D are all elements of the transfer matrix of the cable joint that are the characteristic impedance of the cable joint.
Compared with the prior art, the frequency response modeling method for the high-voltage cable joint considering the broadband characteristic of the semi-conductive shielding layer, provided by the embodiment of the invention, has the advantages that the complex dielectric constant of the inner semi-conductive shielding layer and the outer semi-conductive shielding layer of the cable joint is measured within the preset frequency range, and the complex dielectric constant is fitted along with the frequency change relationship, so that the complex dielectric constant equation of the inner semi-conductive shielding layer and the outer semi-conductive shielding layer of the cable joint is obtained; performing segmentation equivalent processing on the cable joint according to the difference of the internal structure of the cable joint, and establishing a distribution parameter equivalent circuit considering the conductor crimping of the cable joint according to a segmentation result; the frequency domain response characteristic parameters of the cable joint, including characteristic impedance, wave velocity and propagation coefficient, transfer matrix and transmission coefficient, are calculated through a complex dielectric constant equation, the frequency change characteristics of the inner semi-conductive shielding layer and the outer semi-conductive shielding layer of the cable joint can be considered, and the frequency response characteristic of the cable joint is accurately analyzed, so that the propagation characteristic of different central frequency signals at the cable joint and the frequency dependence characteristic of the cable joint can be analyzed according to the frequency domain response characteristic parameters.
Drawings
Fig. 1 is a schematic flow chart of a high-voltage cable joint frequency response modeling method considering broadband characteristics of a semiconductive shielding layer according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the impedance measurement principle provided by the present invention;
FIG. 3 is a schematic structural view of a cable connector provided by the present invention;
FIG. 4 is a schematic view of a segmented left half-axis joint of a cable joint according to the present invention;
FIG. 5 is an equivalent distribution parameter model of each unit of the cable joint provided by the present invention;
FIG. 6 is a graph of inner and outer semiconductive shield parameters versus frequency for a cable joint according to the present invention;
FIG. 7 is a graph of the axial characteristic impedance change of a cable joint at a frequency of 1MHz provided by the present invention;
FIG. 8 is a graph of the change in axial characteristic impedance of a cable joint at different frequencies provided by the present invention;
FIG. 9 is a graph of the change in transmission coefficient amplitude over the range of 1MHz to 100MHz for a cable joint provided by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious 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 obtained by a person skilled in the art without inventive step based on the embodiments of the present invention, are within the scope of protection of the present invention.
Referring to fig. 1, fig. 1 is a schematic flow chart of a high-voltage cable joint frequency response modeling method considering broadband characteristics of a semiconductive shielding layer according to an embodiment of the present invention.
The high-voltage cable joint frequency response modeling method considering the broadband characteristic of the semiconductive shielding layer provided by the embodiment of the invention comprises the following steps of S11 to S15:
step S11, obtaining a first complex dielectric constant and a second complex dielectric constant which are obtained by measuring the preprocessed cable joint inner semi-conductive shielding layer sample and outer semi-conductive shielding layer sample in a preset frequency range.
In specific implementation, the inner semi-conductive shielding layer and the outer semi-conductive shielding layer of the cable joint are respectively sampled to obtain an inner semi-conductive shielding layer sample and an outer semi-conductive shielding layer sample. Illustratively, the specification of the inner semi-conductive shielding layer sample and the outer semi-conductive shielding layer sample can be circular thin sheets with the diameter of 30mm and the thickness of 1mm, and of course, the samples can be processed into other specifications as long as the dielectric constant measurement requirements are met.
Specifically, after the inner semiconductive shielding layer sample and the outer semiconductive shielding layer sample are obtained, the inner semiconductive shielding layer sample and the outer semiconductive shielding layer sample are further pretreated, and the pretreatment process may be: and placing the inner semi-conductive shielding layer sample and the outer semi-conductive shielding layer sample in a drying dish for 24 hours, and taking out the samples to perform gold spraying treatment on the front surface and the back surface of the inner semi-conductive shielding layer sample and the outer semi-conductive shielding layer sample. The inner semi-conductive shielding layer sample and the outer semi-conductive shielding layer sample are pretreated to remove moisture on the surface of the samples as much as possible, and if the step is not carried out, the existence of the moisture can cause the measured dielectric constant value to be lower; the metal spraying treatment is carried out on the front surface and the back surface of the sample so as to eliminate the influence of the surface roughness of the sample on the distribution of an electric field, so that the test electric field is as uniform as possible, and the measurement precision is improved.
For example, the first complex dielectric constant and the second complex dielectric constant of the pretreated cable joint inner semiconductive shielding layer sample and the outer semiconductive shielding layer sample measured in a preset frequency range can be measured by an impedance measurement method, and the preset range can be 1kHz to 100 MHz.
Referring to fig. 2, fig. 2 shows a schematic diagram of the impedance measurement principle. In the context of figure 2, it is shown,voltage signal U flowing through inner semi-conductive shielding layer sample or outer semi-conductive shielding layer sample1The amplitude and phase of (a) can be collected by the vector voltage analyzer 1; current signal I flowing through inner semiconductive shield sample or outer semiconductive shield sampleSSupplied by the inverting input of the operational amplifier and passing through an adjustable resistor RXConverted into a voltage signal U2And collected by a vector voltage analyzer 2; r0To protect the resistance; the sinusoidal signal generator and the vector voltage analyzer are connected to a computer to synchronously calculate the frequency and the phase.
Wherein, the current signal I flowing through the sample for measuring the inner semi-conductive shielding layer or the sample for measuring the outer semi-conductive shielding layerSAnd voltage signal U2The relationship of (1) is:
Figure RE-GDA0003557725920000081
according to the voltage signal U flowing through the inner semi-conductive shielding layer sample or the outer semi-conductive shielding layer sample under different frequency voltages1And a current signal ISThe complex impedance of the inner or outer semiconductive shield samples can be calculated:
Figure RE-GDA0003557725920000082
in the formula (I), the compound is shown in the specification,
Figure RE-GDA0003557725920000083
and
Figure RE-GDA0003557725920000084
for the measured voltage signal U flowing through the test specimen1And calculating the current signal I flowing through the test sampleSIn the form of a complex number.
Thus, the complex dielectric constant of the inner or outer semiconductive shield samples can be expressed as:
Figure RE-GDA0003557725920000085
where ε 'is the real part of the complex permittivity, which is proportional to the reactive current in the medium and has the same meaning as the dielectric constant of the medium, ε' is the imaginary part of the complex permittivity, which is usually used to represent the energy loss due to relaxation polarization in the medium and becomes the loss factor, C0The no-load capacitance of the inner semiconductive shielding layer sample or the outer semiconductive shielding layer sample can be calculated according to the parameters of the inner semiconductive shielding layer sample or the outer semiconductive shielding layer sample, and omega is the angular frequency of the alternating current voltage.
Step S12, fitting the variation relation of the first complex dielectric constant and the second complex dielectric constant along with frequency respectively to obtain a first complex dielectric constant equation corresponding to the inner semi-conductive shielding layer sample and a second complex dielectric constant equation corresponding to the outer semi-conductive shielding layer sample.
In some embodiments, the first complex permittivity equation for the inner semiconductive shield sample and the second complex permittivity equation for the outer semiconductive shield sample can be obtained by fitting the following equations:
Figure RE-GDA0003557725920000091
in the formula, τ1、τ2To relaxation time, σdcIs of direct current conductivity,. epsilon∞Is a high frequency component of dielectric constant, A1、A2、α1、α2Is a fitting constant, epsilon0Is a vacuum dielectric constant of 8.854187817 × 10-12F/m。
It is to be understood that the first complex permittivity equation in the embodiment of the present invention is used to describe the complex permittivity relationship of the inner semiconductive shield sample with respect to frequency, and the second complex permittivity equation is used to describe the complex permittivity relationship of the outer semiconductive shield sample with respect to frequency.
Step S13, according to the difference of the internal structure of the cable connector, the cable connector is processed equivalently in a segmentation mode, and a distribution parameter equivalent circuit considering the crimping of the conductor of the cable connector is established according to the segmentation result; wherein the distributed parameter equivalent circuit includes a plurality of unit circuits.
Referring to fig. 3, fig. 3 shows a schematic structural view of the cable joint. It can be seen that the cable joint contains multiple layers of material inside, such as an outer semiconductive shield, an XPLE primary insulation and an inner semiconductive shield. In practice, the cable joint is divided into a plurality of units according to the change of the internal structure of the cable joint along the axial direction, the segmentation is based on the principle that the structure and the material of each unit are as uniform as possible, for example, when the structure of a certain point is found to be greatly different from the structure before the point, the point is taken as a dividing point to divide the cable joint. As an example, fig. 4 shows a schematic structural diagram of a cable joint after the cable joint is segmented, and from fig. 4, it can be seen that the left half shaft of the cable joint is divided into sections a to f, and a unit circuit corresponding to the unit is established for each unit, so as to obtain an equivalent distribution parameter model of each unit of the cable joint as shown in fig. 5.
Step S14, calculating impedance and admittance of each unit circuit with frequency change by considering the structure and material characteristics of each unit circuit after segmentation and combining the first complex permittivity equation and the second complex permittivity equation.
Step S15, according to the impedance and admittance of each unit circuit along with the frequency change, the characteristic impedance, wave velocity and propagation coefficient of the cable joint along the axial length change under different frequencies are calculated, and according to the characteristic impedance and the propagation coefficient, the transfer matrix and the transmission coefficient of the cable joint are calculated.
In an alternative embodiment, the step S13 "performing a segmentation equivalent process on the cable connector according to the difference in the internal structure of the cable connector, and establishing a distribution parameter equivalent circuit considering the crimping of the conductor of the cable connector according to the segmentation result" specifically includes:
dividing a left half shaft part of the cable joint into a plurality of units which are connected in series according to the internal structure difference of the cable joint and the axial symmetry characteristic of the cable joint; if the unit is a cable joint non-crimping section, the unit is a first unit; if the unit is the cable joint crimping section, the unit is a second unit;
and establishing each first unit circuit corresponding to each first unit and a second unit circuit corresponding to the second unit so as to establish a distributed parameter equivalent circuit considering the crimping of the cable joint conductor.
In the embodiment of the invention, considering that the cable joint has contact resistance at the connection position of the conductors due to crimping, and the contact resistance can cause the radius and the conductivity of the cable core to change, the crimped section needs to be distinguished from other non-crimped sections, the unit of the crimped section is defined as a first unit, and the unit of the non-crimped section is defined as a second unit.
Specifically, the cable joint has an axisymmetric characteristic, and in order to reduce the calculation amount, a left half shaft or a right half shaft portion is taken out, and equivalent segmentation processing is performed on the left half shaft or the right half shaft portion to obtain a plurality of units, wherein the crimping section includes a leftmost section and a rightmost section located in the cable joint, as an example, if a section f in fig. 4 is the crimping section, then a to g are first units, and f is a second unit.
In an alternative embodiment, the step S14 "calculating the impedance and admittance of each unit circuit with frequency according to the first complex permittivity equation and the second complex permittivity equation by considering the structure and material characteristics of each unit circuit after segmentation" specifically includes S141 to S142:
step S141, for each unit circuit, calculating the distribution resistance and the distribution inductance distribution of the unit circuit along with the frequency change, and calculating the impedance of the unit circuit along with the frequency change according to the distribution resistance and the distribution inductance;
s142, calculating the admittance of each material structure layer in the unit circuit along with the change of the frequency, and calculating the admittances of all the material structure layers along with the change of the frequency in parallel to obtain the admittance of the unit circuit along with the change of the frequency; the unit circuit comprises a material structure layer which comprises a main insulating layer and a semi-conductive water-blocking layer, and also comprises at least one of an inner semi-conductive shielding layer and an outer semi-conductive shielding layer, wherein the admittance of the inner semi-conductive shielding layer along with the frequency change is calculated according to the first complex dielectric constant equation, and the admittance of the outer semi-conductive shielding layer along with the frequency change is calculated according to the second complex dielectric constant equation.
In one embodiment, in step S141, the distributed resistance of the unit circuit with frequency variation is calculated by:
when the unit circuit is a first unit circuit, calculating the distributed resistance of the first unit circuit along with the frequency change according to the following formula:
Figure RE-GDA0003557725920000111
when the unit circuit is a second unit circuit, calculating the distributed resistance of the second unit circuit along with the frequency change according to the following formula:
Figure RE-GDA0003557725920000112
Figure RE-GDA0003557725920000113
a′＝a″+Δd
Figure RE-GDA0003557725920000114
wherein R (ω) is the distributed resistance of the first unit, ω is the angular frequency, a1Is the outer radius of the inner conductor, a2Is the inner radius of the outer conductor, p1Is the resistivity of the inner conductor, p2Is the resistivity of the outer conductor, mu0For the vacuum permeability, R' (ω) is the distributed resistance of the second cell, and K is the contact coefficientThe method comprises the following steps of firstly, connecting a cable joint crimping section with a conductor, connecting a cable joint crimping section with a cable body, connecting a cable joint crimping section with a cable, connecting a cable and a cable, wherein a ' is the radius of the conductor of the cable body, a ' is the radius of the conductor of the cable joint crimping section, rho ' is the resistivity of a normal conductor, rho ' is the resistivity of the conductor of the cable joint crimping section, deltad is the thickness of the cable joint crimping section, l is the length of a first unit circuit, and l ' is the length of a second unit circuit.
It is worth to be noted that, in the embodiment of the present invention, in order to accurately calculate the magnitude of the contact resistance of the crimping section of the cable connector, considering that the contact coefficient K is added to measure the change of the resistance value of the section for the second unit, such as the section g in fig. 4, in order to consider that the contact resistance exists at the connection position of the conductor due to the crimping of the cable connector, and the contact resistance may cause the change of the radius and the conductivity of the cable core, so that the resistance value of the second unit may be accurately calculated, and further, the impedance value of the second unit may be accurately calculated.
In one embodiment, in step S141, the distributed inductance of the unit circuit is obtained by:
when the unit circuit is a first unit circuit, calculating the distributed inductance of the first unit circuit according to the following formula:
Figure RE-GDA0003557725920000121
when the unit circuit is a second unit circuit, calculating the distributed inductance of the second unit circuit according to the following formula:
Figure RE-GDA0003557725920000122
Figure RE-GDA0003557725920000123
Figure RE-GDA0003557725920000124
wherein L (ω) is the first unitDistributed inductance of the path, ω angular frequency, a1Is the radius of the conductor of the cable body, a2Inner radius of the outer conductor, mu0For vacuum permeability, p1Is the resistivity of the inner conductor, p2In terms of the resistivity of the outer conductor, L '(ω) is the distributed inductance of the second unit, ρ ″ the conductor resistivity of the cable joint crimping section, a ″ is the radius of the conductor of the cable joint crimping section, Y is the axial length of the cable joint crimping section, L is the length of the first unit circuit, and L' is the length of the second unit circuit.
In the embodiment of the invention, the distributed inductance of each unit circuit is composed of the self-inductance of the inner conductor, the self-inductance of the outer conductor and the mutual inductance between the inner conductor and the outer conductor. For the non-crimping section of the cable joint, namely the first unit, the non-crimping section can be equivalent to an infinite straight conductor for calculation, and the self-inductance of the inner conductor, the self-inductance of the outer conductor and the mutual inductance between the inner conductor and the outer conductor can be accumulated during calculation. For the circuit connector crimping section, namely the second unit, the cable connector crimping section is short in length and is not greatly different from the outer diameter of the cable connector copper shielding layer, so that the circuit connector crimping section cannot be assumed as an infinite-length straight conductor for calculation. Therefore, the cable crimping section is considered to be an infinite conductor, and the inductance calculation of the cable crimping section is corrected. Because the cable crimping section, namely the inductance value of the corresponding area, is not only influenced by the flux linkage generated by the cable crimping section, but also influenced by the flux linkage generated by the semi-infinite long conductors on the two sides, the change of the conductivity of the joint caused by the cable crimping defect can be ignored in the calculation process, the whole cable line is taken as a uniform infinite straight conductor for calculation, the difference value of the crimping section and the normal cable core flux linkage with the same length is subtracted, the total flux linkage of the area is obtained, and then the inductance value is solved.
The distributed inductance of each unit after the cable joint is segmented can be obtained, and then the inductance value of the whole circuit joint can be calculated
Figure RE-GDA0003557725920000131
(L here)1，L2Refers to the distributed inductance of each unit circuit),the inductance value of the whole cable joint can be obtained.
Further, the impedance of the unit circuit with frequency change is calculated by the following formula:
Z＝R+jωL
wherein, L is the distributed resistance of each unit circuit, and L is the distributed inductance of each unit circuit. When the unit circuit is a first unit circuit, L is the distributed inductance L (ω) of the first unit circuit, and when the unit circuit is a second unit circuit, L is the distributed inductance L' (ω) of the second unit circuit.
In one embodiment, in step S142 ", the admittance of each material structure layer in the unit circuit with the frequency is calculated, and the admittances of all the material structure layers with the frequency are calculated in parallel, so as to obtain the admittance of the unit circuit with the frequency; the unit circuit comprises a material structure layer which comprises a main insulating layer, a semiconductive water resisting layer and at least one of an inner semiconductive shielding layer and an outer semiconductive shielding layer, wherein the admittance of the unit circuit along with the frequency change is calculated according to the following formula:
Figure RE-GDA0003557725920000141
wherein, YiIs the admittance of a structural layer of material.
Exemplary, let Y1Being admittance of the inner semiconductive shield layer, Y2Being admittance of the outer semiconductive shield, Y3Is the admittance of the main insulating layer, Y4Is a semiconductive water-blocking layer admittance. Then in some embodiments:
when the unit circuit comprises the main insulating layer, the semi-conductive water-blocking layer and the inner semi-conductive shielding layer, the admittance of the unit circuit with the frequency change is as follows:
Figure RE-GDA0003557725920000142
when the unit circuit includes a main insulating layer, a semi-conductive water blocking layer and an outer semi-conductive shielding layer, the unit circuit varies with frequencyThe admittance of the chemo is:
Figure RE-GDA0003557725920000143
when the unit circuit comprises the main insulating layer, the semi-conductive water-blocking layer, the inner semi-conductive shielding layer and the outer semi-conductive shielding layer, the admittance of the unit circuit with the frequency change is as follows:
Figure RE-GDA0003557725920000144
in one embodiment, the admittance of the inner semiconductive shield with respect to frequency is calculated according to the first complex permittivity equation, and the admittance of the outer semiconductive shield with respect to frequency is calculated according to the second complex permittivity equation, specifically:
the admittance of the inner semiconductive shield layer is calculated according to the following equation:
Figure RE-GDA0003557725920000145
the admittance of the outer semiconductive shield is calculated according to the following equation:
Figure RE-GDA0003557725920000146
wherein G is1(omega) is the admittance of the inner semiconducting shield layer, omega is the angular frequency, epsilon0In order to have a dielectric constant in a vacuum,
Figure RE-GDA0003557725920000147
is a first complex permittivity equation, ro1Is the outer radius of the inner semiconductive shield layer, ri1Is the inner radius of the inner semiconductive shield layer, Y2(ω) is the admittance of the outer semiconductive shield layer,
Figure RE-GDA0003557725920000151
is a second complex permittivity equation, ro2Outside the outer semiconductive shield layerRadius ri2The inner radius of the outer semiconductive shield layer.
In some embodiments, the admittance of the main insulating layer and the admittance of the semi-conductive water barrier are both based on
Figure RE-GDA0003557725920000152
Calculating, wherein n is 3, 4; and is
Figure RE-GDA0003557725920000153
The value of (c) can be directly obtained by the prior art.
In one embodiment, the step S15 ″ calculates the characteristic impedance, wave velocity and propagation coefficient of the cable joint along the axial length at different frequencies according to the impedance and admittance of each unit circuit varying with the frequency, and calculates the characteristic impedance Z in the transfer matrix and transmission coefficient of the cable joint according to the characteristic impedance and the propagation coefficient0The wave velocity v and the propagation coefficient γ are calculated as follows:
Figure RE-GDA0003557725920000154
Figure RE-GDA0003557725920000155
Figure RE-GDA0003557725920000156
wherein Z is the impedance of the unit circuit, Y is the admittance of the unit circuit, and C is the capacitance in parallel with the conductance in the unit circuit.
In one embodiment, the transfer matrix of the cable joint is calculated by:
the cable joint is equivalent to a plurality of units which are coaxially connected in series, and the transfer matrix characteristic parameters of each unit are calculated according to the propagation coefficient, the axial length and the characteristic impedance corresponding to each unit;
and calculating the product of the transfer matrix characteristic parameters of all the units to obtain the transfer matrix of the cable joint.
In one embodiment, the transfer matrix characterization parameter of the cell is calculated by the following formula:
Figure RE-GDA0003557725920000157
wherein the content of the first and second substances,
Figure RE-GDA0003557725920000161
characteristic parameter of transfer matrix, gamma, representing the ith celliIs the propagation coefficient corresponding to the ith unit circuit in the equivalent circuit, liIs the axial length of the i-th cell, ZoiThe characteristic impedance corresponding to the ith unit circuit in the equivalent circuit.
Specifically, in the actual circuit, both ends of the cable connector are connected with the cable body, and when the traveling wave refraction and reflection are considered, the reference impedances at both ends of the connector equivalent two-port network can be set as the characteristic impedance of the cable body. Further, in one embodiment, the transmission coefficient of the cable joint is calculated by the following formula:
Figure RE-GDA0003557725920000162
wherein, TjIs the transmission coefficient of the cable joint, ZoA, B, C, D are all elements of the transfer matrix of the cable joint that are the characteristic impedance of the cable joint.
In a primary experiment, the frequency response modeling method of the high-voltage cable joint considering the broadband characteristic of the semiconductive shielding layer provided by the embodiment of the invention is carried out on the integral prefabricated high-voltage cable joint with the cable model of YJLW03-Z-64/110kV-1 × 630mm2, and the change condition of the parameters of the inner semiconductive shielding layer and the outer semiconductive shielding layer of the cable joint along with the frequency as shown in FIG. 6 is obtained.
Based on the measured data of the inner semi-conductive shielding layer and the outer semi-conductive shielding layer, a broadband dielectric constant equation of the inner semi-conductive shielding layer and the outer semi-conductive shielding layer of the cable joint is obtained through mathematical fitting, and the broadband dielectric constant equation is substituted into a distribution parameter model of the cable joint to calculate the frequency response characteristic parameters of the distribution parameter model. Fig. 7 shows the characteristic axial impedance variation of the cable joint of the through joint at the frequency of 1 MHz.
The characteristic impedance of the joint along the axial direction at different frequencies is shown in the following figure 8, and it can be seen from the figure that although the characteristic impedance of the cable joint has a significant variation trend along the axial distance, the frequency variation parameters of the cable joint keep good consistency in a high-frequency range and have a low frequency dependence characteristic.
According to the transfer matrix and the transmission coefficient, the transmission coefficient amplitude of the cable joint in the range of 1 MHz-100 MHz as shown in FIG. 9 can be calculated. The amplitude of the transmission coefficient of the intermediate joint is attenuated in an oscillating manner as a whole along with the increase of the signal frequency, and when the signal frequency is 100MHz, the amplitude of the transmission coefficient is about 0.85.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.

Claims (9)

1. A frequency response modeling method of a high-voltage cable joint considering broadband characteristics of a semiconductive shielding layer is characterized by comprising the following steps:
obtaining a first complex dielectric constant and a second complex dielectric constant which are obtained by measuring the preprocessed sample of the inner semi-conductive shielding layer and the preprocessed sample of the outer semi-conductive shielding layer in a preset frequency range;
respectively fitting the variation relation of the first complex dielectric constant and the second complex dielectric constant along with the frequency to obtain a first complex dielectric constant equation corresponding to the inner semi-conductive shielding layer sample and a second complex dielectric constant equation corresponding to the outer semi-conductive shielding layer sample;
performing segmentation equivalent processing on the cable joint according to the difference of the internal structure of the cable joint, and establishing a distribution parameter equivalent circuit considering the conductor crimping of the cable joint according to a segmentation result; wherein the distributed parameter equivalent circuit comprises a plurality of unit circuits;
calculating the impedance and admittance of each unit circuit along with the change of frequency by considering the structure and material characteristics of each unit after segmentation and combining the first complex dielectric constant equation and the second complex dielectric constant equation;
and calculating the characteristic impedance, wave speed and propagation coefficient of the cable joint along the axial length under different frequencies according to the impedance and admittance of each unit circuit along with the frequency change, and calculating the transfer matrix and transmission coefficient of the cable joint according to the characteristic impedance and the propagation coefficient.
2. The method for modeling the frequency response of the high-voltage cable joint considering the broadband characteristic of the semiconductive shielding layer according to claim 1, wherein the step of performing the sectional equivalent processing on the cable joint according to the difference of the internal structure of the cable joint and establishing the distribution parameter equivalent circuit considering the conductor crimping of the cable joint according to the sectional result specifically comprises the steps of:
dividing a left half shaft part of the cable joint into a plurality of units which are connected in series according to the internal structure difference of the cable joint and the axial symmetry characteristic of the cable joint; if the unit is a cable joint non-crimping section, the unit is a first unit; if the unit is a cable joint crimping section, the unit is a second unit;
and establishing each first unit circuit corresponding to each first unit and a second unit circuit corresponding to the second unit so as to establish a distributed parameter equivalent circuit considering the crimping of the cable joint conductor.
3. The method according to claim 1 or 2, wherein the step of calculating the impedance and admittance of each unit circuit with frequency change by considering the structural and material properties of each unit circuit after segmentation and combining the first complex permittivity equation and the second complex permittivity equation comprises:
for each unit circuit, calculating the distribution resistance and the distribution inductance distribution of the unit circuit along with the frequency change, and calculating the impedance of the unit circuit along with the frequency change according to the distribution resistance and the distribution inductance;
calculating the admittance of each material structure layer in the unit circuit along with the change of the frequency, and performing parallel calculation on the admittances of all the material structure layers along with the change of the frequency to obtain the admittance of the unit circuit along with the change of the frequency; the unit circuit comprises a material structure layer, an inner semi-conductive shielding layer and an outer semi-conductive shielding layer, wherein the material structure layer comprises a main insulating layer and a semi-conductive waterproof layer, and at least one of the inner semi-conductive shielding layer and the outer semi-conductive shielding layer, the admittance of the inner semi-conductive shielding layer changing along with the frequency is obtained by calculation according to the first complex dielectric constant equation, and the admittance of the outer semi-conductive shielding layer changing along with the frequency is obtained by calculation according to the second complex dielectric constant equation.
4. The method for modeling the frequency response of the high-voltage cable joint considering the broadband characteristic of the semiconductive shielding layer according to claim 3, wherein the distributed resistance of the unit circuit with frequency variation is calculated by:
when the unit circuit is a first unit circuit, calculating the distributed resistance of the first unit circuit along with the frequency change according to the following formula:
Figure RE-FDA0003557725910000021
when the unit circuit is a second unit circuit, calculating the distributed resistance of the second unit circuit along with the frequency change according to the following formula:
Figure RE-FDA0003557725910000022
Figure RE-FDA0003557725910000031
a′＝a″+Δd
Figure RE-FDA0003557725910000032
wherein R (ω) is the distributed resistance of the first unit, ω is the angular frequency, a1Is the outer radius of the inner conductor, a2Is the inner radius of the outer conductor, p1Is the resistivity of the inner conductor, p2Is the resistivity of the outer conductor, mu0For the vacuum permeability, R '(ω) is the distributed resistance of the second unit, K is the contact coefficient, a' is the conductor radius of the cable body, a "is the radius of the conductor of the cable joint crimping section, ρ 'is the normal conductor resistivity, ρ" is the conductor resistivity of the cable joint crimping section, Δ d is the thickness of the cable joint crimping section, l is the length of the first unit circuit, and l' is the length of the second unit circuit.
5. The method for modeling the frequency response of the high-voltage cable joint considering the broadband characteristic of the semiconductive shielding layer according to claim 3, wherein the distributed inductance of the unit circuit is obtained by:
when the unit circuit is a first unit circuit, calculating the distributed inductance of the first unit circuit according to the following formula:
Figure RE-FDA0003557725910000033
when the unit circuit is a second unit circuit, calculating the distributed inductance of the second unit circuit according to the following formula:
Figure RE-FDA0003557725910000034
Figure RE-FDA0003557725910000035
Figure RE-FDA0003557725910000036
wherein L (ω) is the distributed inductance of the first unit circuit, ω is the angular frequency, a1Is the radius of the conductor of the cable body, a2Inner radius of the outer conductor, mu0For vacuum permeability, p1Is the resistivity of the inner conductor, p2In terms of the resistivity of the outer conductor, L '(ω) is the distributed inductance of the second unit, ρ ″ the conductor resistivity of the cable joint crimping section, a ″ is the radius of the conductor of the cable joint crimping section, Y is the axial length of the cable joint crimping section, L is the length of the first unit circuit, and L' is the length of the second unit circuit.
6. The method for modeling the frequency response of the high-voltage cable joint considering the broadband characteristic of the semi-conductive shielding layer according to claim 3, wherein the frequency-dependent admittance of the inner semi-conductive shielding layer is calculated according to the first complex permittivity equation, and the frequency-dependent admittance of the outer semi-conductive shielding layer is calculated according to the second complex permittivity equation, specifically:
the admittance of the inner semiconductive shield layer is calculated according to the following equation:
Figure RE-FDA0003557725910000041
the admittance of the outer semiconductive shield is calculated according to the following equation:
Figure RE-FDA0003557725910000042
wherein, Y1(omega) isAdmittance of the inner semiconducting shield layer, omega being angular frequency, epsilon0In order to have a dielectric constant in a vacuum,
Figure RE-FDA0003557725910000043
is a first complex permittivity equation, ro1Is the outer radius of the inner semiconductive shield layer, ri1Is the inner radius of the inner semiconductive shield layer, Y2(ω) is the admittance of the outer semiconductive shield layer,
Figure RE-FDA0003557725910000044
is a second complex permittivity equation, ro2Is the outer radius of the outer semiconductive shield layer, ri2Is the inner radius of the outer semiconducting shield layer, j is the imaginary unit.
7. The method for modeling the frequency response of the high-voltage cable joint considering the broadband characteristic of the semiconductive shielding layer according to claim 1, wherein the transfer matrix of the cable joint is calculated by the following steps:
the cable joint is equivalent to a plurality of units which are coaxially connected in series, and the transfer matrix characteristic parameters of each unit are calculated according to the propagation coefficient, the axial length and the characteristic impedance corresponding to each unit;
and calculating the product of the transfer matrix characteristic parameters of all the units to obtain the transfer matrix of the cable joint.
8. The method of claim 7, wherein the transfer matrix characteristic parameters of the unit are calculated by the following formula:
Figure RE-FDA0003557725910000051
wherein the content of the first and second substances,
Figure RE-FDA0003557725910000052
characteristic parameter of transfer matrix, gamma, representing the ith celliIs the propagation coefficient corresponding to the ith unit circuit in the equivalent circuit, liIs the axial length of the i-th cell, ZoiThe characteristic impedance corresponding to the ith unit circuit in the equivalent circuit.
9. The method of claim 8, wherein the transmission coefficient of the cable joint is calculated by the following formula:
Figure RE-FDA0003557725910000053
wherein, TjIs the transmission coefficient of the cable joint, ZoA, B, C, D are all elements of the transfer matrix of the cable joint that are the characteristic impedance of the cable joint.
CN202111516218.9A 2021-12-08 2021-12-08 High-voltage cable joint frequency response modeling method considering broadband characteristic of semi-conductive shielding layer Pending CN114492284A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111516218.9A CN114492284A (en) 2021-12-08 2021-12-08 High-voltage cable joint frequency response modeling method considering broadband characteristic of semi-conductive shielding layer

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111516218.9A CN114492284A (en) 2021-12-08 2021-12-08 High-voltage cable joint frequency response modeling method considering broadband characteristic of semi-conductive shielding layer

Publications (1)

Publication Number Publication Date
CN114492284A true CN114492284A (en) 2022-05-13

Family

ID=81492097

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111516218.9A Pending CN114492284A (en) 2021-12-08 2021-12-08 High-voltage cable joint frequency response modeling method considering broadband characteristic of semi-conductive shielding layer

Country Status (1)

Country Link
CN (1) CN114492284A (en)

Similar Documents

Publication Publication Date Title
CN107607837B (en) Cable insulation aging degree testing method and device based on impulse voltage
US7970559B2 (en) Identifying damage to a wire
CN114019309B (en) Cable defect positioning method based on frequency domain reflection technology
CN109165446B (en) Method for calculating sensitivity of long cable inlet impedance to insulation aging
Mo et al. The possibility of fault location in cross-bonded cables by broadband impedance spectroscopy
CN113419147A (en) Radar spectrum diagram based visualized cable insulation state diagnosis and evaluation method
CN115372747A (en) Cable aging degradation state detection method and aging monitoring device
CN114047409A (en) Power cable local defect online positioning method based on electromagnetic coupling injection
CN115453261A (en) Cable defect detection method based on synchronous compression wavelet transform
Hu et al. Principle and verification of an improved algorithm for cable fault location based on complex reflection coefficient spectrum
Shan et al. Effect of segmented thermal aging on defect location accuracy in XLPE distribution cables
Kostiukov Measurement of dissipation factor of inner layers of insulation in three-core belted cables
Chi et al. Research on condition assessment of XLPE cable based on signal propagation characteristics
Norouzi et al. Effect of cable joints on frequency domain analysis
CN114492284A (en) High-voltage cable joint frequency response modeling method considering broadband characteristic of semi-conductive shielding layer
Fritsch et al. Measurable bandwidth of partial discharges on medium voltage cables
Hashmi et al. Covered-conductor overhead distribution line modeling and experimental verification for determining its line characteristics
CN114675128A (en) Submarine cable insulation fault on-line positioning method based on sheath current and voltage
Das et al. Investigations on feasibility of fault detection in underground power cables using SFRA
CN114062852A (en) Cable intermediate joint fault diagnosis method, device, equipment and readable storage medium
Hassen et al. A stranded Unshielded Twisted Pair modeling for online fault location using OMTDR-based diagnosis sensor
Eriksson et al. Localization of insulation degradation in medium voltage distribution cables
Mo et al. Fault location for coaxial cables based on broadband impedance spectroscopy
Lee et al. Characteristics of high frequency partial discharge for artificially defected extra high voltage accessories
Mugala Influence of the semi-conducting screens on the wave propagation characteristics of medium voltage extruded cables

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination