CN113138325B - Rapid diagnosis method for loss decoupling of insulating low-frequency medium of crosslinked polyethylene cable - Google Patents
Rapid diagnosis method for loss decoupling of insulating low-frequency medium of crosslinked polyethylene cable Download PDFInfo
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- CN113138325B CN113138325B CN202110400609.8A CN202110400609A CN113138325B CN 113138325 B CN113138325 B CN 113138325B CN 202110400609 A CN202110400609 A CN 202110400609A CN 113138325 B CN113138325 B CN 113138325B
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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
- G01R31/12—Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing
- G01R31/1227—Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing of components, parts or materials
- G01R31/1263—Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing of components, parts or materials of solid or fluid materials, e.g. insulation films, bulk material; of semiconductors or LV electronic components or parts; of cable, line or wire insulation
- G01R31/1272—Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing of components, parts or materials of solid or fluid materials, e.g. insulation films, bulk material; of semiconductors or LV electronic components or parts; of cable, line or wire insulation of cable, line or wire insulation, e.g. using partial discharge measurements
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- 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
- G01R27/26—Measuring inductance or capacitance; Measuring quality factor, e.g. by using the resonance method; Measuring loss factor; Measuring dielectric constants ; Measuring impedance or related variables
- G01R27/2688—Measuring quality factor or dielectric loss, e.g. loss angle, or power factor
- G01R27/2694—Measuring dielectric loss, e.g. loss angle, loss factor or power factor
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Abstract
The method for quickly diagnosing the loss decoupling of the insulating low-frequency medium of the cross-linked polyethylene cable is characterized by comprising the following steps of: the method comprises the following steps: firstly, measuring the polarization current value of the cable; then, performing time-frequency domain conversion by expanding a Debye model, rapidly converting the measured polarization current value into a dielectric parameter under a corresponding frequency domain, and obtaining an integral dielectric loss factor tan delta of the XLPE cable insulation; on the basis, the integral dielectric loss factor is split to obtain the conductance loss and the polarization loss, and the polarization loss tan delta caused by the water tree defect is extracted by expanding the polarization branch caused by the water tree defect represented on the Debye model p3 (ii) a By contrast tan delta around the peak frequency p3 The magnitude of the value determines the cable aging status. The invention can quickly diagnose the aging state of the cable on site, not only can shorten the diagnosis time to a greater extent, but also can accurately reflect the aging state of the cable.
Description
Technical Field
The invention relates to the field of insulation material aging evaluation methods, in particular to a rapid diagnosis method for insulation low-frequency dielectric loss decoupling of a crosslinked polyethylene cable. It can be quickly diagnosed about the state of aging of the crosslinked polyethylene cable.
Background
Crosslinked polyethylene cables (XLPE cables) are widely used in urban power transmission lines. However, in practical application, XLPE cables are easily affected by various factors such as mechanical damage, moisture infiltration, chemical corrosion and the like, so that the cable insulation is gradually deteriorated, even insulation failure and the like occur, and thus power grid power failure accidents are caused. Statistics show that water tree aging is the main cause of cable system failure. Therefore, the detection and evaluation of the insulation state of the XLPE cable have important significance for urban power supply reliability.
The FDS test time of the low frequency band can be as long as several hours, the cable belongs to distributed equipment, the length is long, a high-capacity power supply is required even under the low frequency test, and the FDS test system is inconvenient to carry and is not convenient for field off-line diagnosis. The PDC method (based on a short-time polarization/depolarization current method) has the advantages of direct current detection, low power supply capacity and the like, insulated time domain information is directly obtained, dielectric parameters in a frequency domain are obtained by using a time-frequency domain dielectric parameter conversion principle, and the test time can be greatly reduced.
The literature research shows that the existing time-frequency domain conversion method can only obtain the integral dielectric loss factor spectrum of the cable and cannot distinguish the types in the integral loss in detail in the application of the diagnosis of the insulation aging state of the cable. The existing literature shows that the Fourier transform method is widely applied, but the loss characteristic in a lower frequency range is not studied temporarily, and the invention utilizes a brand-new extended Debye model to decouple the loss of the cable insulation at the ultra-low frequency. It is therefore necessary to study the loss characteristics of XLPE cable insulation at lower frequencies.
Disclosure of Invention
Aiming at the defects of the prior art in the field of cable aging diagnosis, the invention provides a rapid diagnosis method for decoupling the insulation low-frequency dielectric loss of a crosslinked polyethylene cable. The method aims to greatly reduce the test time and quickly obtain the dielectric parameters in the frequency domain through a time-frequency domain conversion technology, thereby improving the detection efficiency and accurately judging the aging state of the cable. The method aims to realize rapid and accurate evaluation of the insulation aging state of the crosslinked polyethylene cable.
The object of the invention is achieved by the following measures: the method for quickly diagnosing the loss decoupling of the insulating low-frequency medium of the crosslinked polyethylene cable is characterized by comprising the following steps of: the method comprises the following steps:
(1) firstly, measuring the polarization current value of the cable;
(2) then, performing time-frequency domain conversion by expanding a Debye model, quickly converting the measured polarization current value into dielectric parameters (namely frequency domain parameters) in a corresponding frequency domain, and obtaining an integral dielectric loss factor tan delta of the XLPE cable insulation;
(3) on the basis, the integral dielectric loss factor is split to obtain the conductance loss and the polarization loss, and the polarization loss tan delta caused by the water tree defect is extracted by expanding a polarization branch circuit caused by characterizing the water tree defect on a Debye model p3 ；
(4) By contrast tan delta around the peak frequency p3 The value size judges the cable aging state.
In the above technical solution, the specific method of step (2) is:
respectively representing different types of polarization processes by using a plurality of resistor-capacitor series branches by using an extended Debye model; three branches in the extended Debye model respectively represent three polarization processes contained in the insulation of the equivalent XLPE cable, and in the third-order model, C 0 Represents the cable insulator capacitance; r is 0 Representing a cable leakage resistance; r is 1 、C 1 A branch parameter representing polarization of the cable insulating material body; r is 2 、C 2 Is a parameter representing a branch circuit for representing the polarization of an amorphous and crystal interface; r 3 、C 3 Representing polarization branch parameters caused by characterizing water tree defects;
the complex capacitance C (ω) can be calculated by extending the three branches in the Debye model:
the overall dielectric loss factor can be obtained according to the ratio of the imaginary part to the real part of the complex capacitance:
measuring the polarization current of 1800s duration, and quickly converting time domain parameters into cable insulation frequency domain information with the frequency range of 0.001Hz-0.5Hz by using an extended Debye model;
by the Nyquist theorem of sampling
Wherein fs is the sampling frequency; f is the frequency resolution; fc is the maximum recoverable signal frequency; n is the number of measurement points;
in the above technical solution, in the step (3), the integral dielectric loss of the cable insulation is split to obtain the polarization loss part, and based on the decoupling method of the extended Debye model, a conductance loss expression is obtained first:
when a sinusoidal voltage U (ω) is applied to the insulation, the current flowing through the insulation of the cable can be expressed as:
I(ω)＝jω[C'(ω)-jC″(ω)]U(ω)
＝jωC a [ε'(ω)-jε″(ω)]U(ω)；
in the formula C a A vacuum geometry capacitor for cable insulation;
the real and imaginary parts of the complex permittivity can be expressed as:
at ω R i C i <<1 and C 0 >>C i When the temperature of the water is higher than the set temperature,
the complex dielectric constant can be expressed as
In the formula epsilon r The relative dielectric constant of the cable insulation;
by
Wherein d is the thickness of the cable insulation; s is the area of cable insulation; sigma 0 Electrical conductivity for cable insulation; vacuum geometric capacitor C for cable insulation a And a leakage resistance R 0 Can be represented by the actual parameters of the cable as:
wherein a and b are the radius of the inner and outer conductors of the cable; l is the cable length; sigma 0 The electrical conductivity of the cable insulation.
The conductance loss based on the extended debye model can therefore be further expressed as:
the polarization loss part is the dielectric loss factor of the whole cable insulation minus the conductance loss part.
In the above technical solution, in the step (4), the polarization loss tan δ caused by the water tree defect p3 The relationship between the size of (2) and the aging state of the cable water tree is as follows: said polarization loss tan delta around the peak frequency p3 The larger the value of (A), the more the cable water tree deteriorates.
According to the method, the time domain parameters of the polarization current are quickly converted into corresponding frequency domain information by using the extended Debye model through a quick diagnosis method for decoupling the insulation low-frequency dielectric loss of the cross-linked polyethylene cable under low frequency, so that the polarization loss and the conductance loss of the dielectric loss of the cable are effectively distinguished, and the polarization loss caused by the water tree defect is extracted. Calculating to obtain the polarization loss (tan delta) caused by water tree defects in the cable insulating material p3 ) The size of the peak value is used for diagnosis, so that the measurement time of the polarization current is greatly shortened, the diagnosis time is shortened, and the aging condition of the cable can be accurately reflected.
Meanwhile, the metal leakage-proof rings are additionally arranged at the two ends of the cable, and the two metal leakage-proof rings are connected by using the lead to prevent the surface current from entering the ammeter, so that the influence of the surface current on a measurement value is reduced.
The invention provides a rapid diagnosis method for decoupling the insulation low-frequency dielectric loss of a cross-linked polyethylene cable, which is characterized in that a Debye model is expanded to rapidly convert time domain parameters of cable polarization current measured based on a PDC method to obtain cable insulation frequency domain information, so that the integral dielectric loss factor of cable insulation is obtained. On the basis of the aboveThe integral dielectric loss factor is split to obtain the conductance loss and the polarization loss, and the polarization loss tan delta caused by the water tree defect is further extracted p3 Comparison of tan delta around the peak frequency p3 The value size judges the cable aging state. The invention can quickly diagnose the aging state of the cable on site, not only can shorten the diagnosis time to a greater extent, but also can accurately reflect the aging state of the cable.
Drawings
Fig. 1 is a schematic view of polarization current measurement of a crosslinked polyethylene cable provided by an embodiment of the present invention;
FIG. 2 is a flow chart of the rapid field diagnosis of aging of a crosslinked polyethylene cable according to an embodiment of the present invention;
FIG. 3 is a branch diagram of an extended Debye model provided by an embodiment of the invention;
fig. 4 is a spectrum of loss factors of polarized media of XLPE cables due to water tree defects under different aging levels according to an embodiment of the present invention.
Detailed Description
The embodiments of the present invention will be described in detail with reference to the drawings, but the present invention is not limited to these embodiments. While the advantages of the invention will be apparent and readily appreciated by the description. In addition, the technical features involved in the respective embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
FIG. 1 is a schematic view of a polarization current measurement of a crosslinked polyethylene cable; wherein the measuring time of the polarization current is 1800s, and the lower limit frequency of 0.001Hz can be obtained after time-frequency domain conversion by the Nyquist sampling theorem; the shorter the measuring time is, the smaller the frequency range of the dielectric loss factor of the whole cable insulation is, the lower limit frequency is set to be 0.001Hz, and the upper limit frequency can be slightly changed according to the actual situation. In FIG. 1, 11 is a first metal leakage-proof ring, 12 is a second metal leakage-proof ring, 2 is a cable conductor, 3 is a DC high voltage power supply, C is a capacitor, K 1 Is a first switch, K 2 For the second switch, R1 was 1M Ω, R2 was 500M Ω, R3 was 200M Ω, and the electrometer was Keithley 6517B.
The cable polarization current is measured using the measure polarization current circuit shown in fig. 1. The output end of the direct-current high-voltage power supply 3 is connected with the wire core of the cable conductor 2 to measure the polarization current. On the basis of additionally arranging a first metal leakage-proof ring 11 and a second metal leakage-proof ring 12 at two ends of a cable, the first metal leakage-proof ring and the second metal leakage-proof ring are connected by using a lead so as to prevent the surface current from entering an ammeter, thereby reducing the influence of the surface current on a measurement value. The parts of the edge surfaces at the two ends of the cable are wiped by absolute ethyl alcohol before and after carrying out a PDC experiment, so that the influence of the edge surface leakage current on the actual current value in the test process is reduced.
Fig. 2 is a flow chart of the rapid field diagnosis of the aging of the crosslinked polyethylene cable according to the present invention, and it can be known from fig. 2 that: the method comprises the following steps: measuring the polarization current for 1800s, wherein the measuring method is as shown in figure 1; the second step: converting the polarization current into a cable integral dielectric loss factor tan delta under the corresponding frequency by expanding a Debye model; the third step: splitting the integral dielectric loss factor of the cable to obtain a polarization loss part, and extracting the polarization loss tan delta caused by water tree defects based on an extended Debye model p3 (ii) a The fourth step: by comparing the polarization losses tan delta near the peak frequency p3 The aging state of the cable is judged according to the size of the cable. The invention shortens the measurement time of the polarization current to a greater extent, shortens the diagnosis time and can accurately reflect the aging condition of the cable.
FIG. 3 is a branch diagram of the extended Debye model of the present invention; in the figure C 0 Represents the cable insulator capacitance; r 0 Representing a cable leakage resistance; r is 1 、C 1 Is a branch parameter representing the polarization of the cable insulating material (i.e. the polarization of the interface formed by the semiconductive layer and XLPE); r is 2 、C 2 Is a parameter representing a branch characterizing the polarization of an amorphous and crystalline interface; r is 3 、C 3 To represent the polarization branch parameters characterizing the water tree defect. And respectively representing different types of polarization processes by using a plurality of resistance-capacitance series branches by using an extended Debye model. And fitting the measured polarization current to obtain parameters of each branch in the extended Debye model, so as to obtain the integral dielectric loss factor spectrum of the cable. Three branches in the extended Debye model respectively represent equivalent XLPE cablesThree polarization processes are contained inside the insulation.
FIG. 4 shows the loss factor spectra of polarized media caused by water tree defects of XLPE cable under different aging degrees. In the embodiment of the invention, the actual aging degree A1 of the cable<A2<A3. It can be seen from fig. 4 that as the aging degree of the cable sample increases, the polarization loss of the third branch gradually increases, and the polarization loss tan δ of the same type of cable (a2, A3 are the same type of cable, a1 is another type of cable, three cables are the same type, except that a1 is not subjected to aging treatment) is increased p3 The frequency of its peak is relatively close.
The invention provides a method for quickly diagnosing the loss decoupling of an insulating low-frequency medium of a cross-linked polyethylene cable, which comprises the following steps: (1) firstly, measuring the polarization current value of the cable;
(2) polarization current values were plotted using Origin software and then fitted to obtain parameters for each branch in the extended Debye model. Then, performing time-frequency domain conversion by expanding a Debye model, and rapidly converting the measured polarization current value into dielectric parameters (namely frequency domain parameters) in a corresponding frequency domain to obtain an integral insulation dielectric loss factor tan delta of the XLPE cable;
(3) on the basis, the integral dielectric loss factor is split to obtain the conductance loss and the polarization loss, and the polarization loss tan delta caused by the water tree defect is extracted by expanding the polarization branch caused by the water tree defect represented on the Debye model p3 ，
(4) By contrast tan delta around the peak frequency p3 The magnitude of the value determines the cable aging status.
The method can realize the rapid diagnosis of the aging state of the cable on site, can shorten the time required by the diagnosis to a greater extent, and can accurately reflect the aging state of the cable.
The method for converting the time domain parameters into the frequency domain parameters by extending the Debye model in the step (1) comprises the following steps:
respectively representing different types of polarization processes by using a plurality of resistor-capacitor series branches by using an extended Debye model; fitting the measured polarization current to obtain parameters of each branch in the extended Debye modelThen, the integral dielectric loss factor spectrum of the cable can be obtained according to the existing formula; three branches in the extended Debye model respectively represent three polarization processes contained in the insulation of the equivalent XLPE cable, and in the third-order model, C 0 Represents the cable insulator capacitance; r is 0 Representing a cable leakage resistance; r is 1 、C 1 Is a branch parameter representing the bulk polarization of the cable insulation (i.e. the interfacial polarization formed by the semiconducting layer and the XLPE); r 2 、 C 2 Is a parameter representing a branch characterizing the polarization of an amorphous and crystalline interface; r 3 、C 3 To represent the parameters characterizing the polarization branches caused by water tree defects, as shown in FIG. 3.
The complex capacitance C (ω) can be calculated by extending the three branches in the Debye model:
c represents complex capacitance, C 'represents the real part of the complex capacitance, C' represents the imaginary part of the complex capacitance, j is the complex field, C 0 、R 0 The above characters have shown that the accumulation symbol is the addition of the expressions of the capacitance and the resistance corresponding to the three branches.
The overall dielectric loss factor can be obtained according to the ratio of the imaginary part to the real part of the complex capacitance:
the invention measures the polarization current with the duration of 1800s, and the frequency is 1 Hz. And rapidly converting the time domain parameters into cable insulation frequency domain information with the frequency range of 0.001Hz-0.5Hz by using an extended Debye model.
The diagnosis method greatly reduces the test time, improves the detection efficiency and can accurately judge the aging state of the cable water tree on site.
The method combines the PDC method and the FPS method, converts the polarization current value measured by the PDC method into corresponding frequency domain parameters through a time-frequency domain, and if only one method is used for diagnosis, the low-frequency parameters can take tens of hours of measurement time. And within 0.001Hz to 0.01Hz, the loss peak appears in the sample dielectric loss, and the result is visual and reliable.
By utilizing the time-frequency domain conversion method of the extended Debye model, the cable insulation polarization current value obtained based on the polarization/depolarization current method can be quickly converted to obtain the dielectric loss information in the frequency domain, and the test time can be greatly reduced. And respectively equivalent three polarization processes contained in the XLPE cable insulation by using the resistor-capacitor series branch, comparing the virtual part and the real part of the complex capacitor to obtain an integral dielectric loss expression of the cable, and combining the derived conductance loss part to directly obtain a polarization loss part.
Integral dielectric loss factor of cable insulation:
extracting a polarization loss part of a third branch (a polarization loss part caused by water tree defects) according to the polarization process corresponding to each branch in the extended Debye model:
the invention has the advantages that the derivative is given, and the whole dielectric loss factor spectrum of the cable can be quickly obtained by directly substituting the corresponding parameter values during operation.
In the step (2), the integral dielectric loss of the cable insulation is split to obtain a polarization loss part, and a conductance loss expression is obtained firstly based on a decoupling method of an extended Debye model:
when a sinusoidal voltage U (ω) is applied to the insulation, the current flowing through the insulation of the cable can be expressed as:
in the formula, Ca is a vacuum geometric capacitance of cable insulation; u (omega) is sinusoidal voltage, I (omega) is sinusoidal current, j is a complex field, omega angular frequency, C 'is a real part of complex capacitance, C' is an imaginary part of complex capacitance, epsilon 'is a real part of complex permittivity, epsilon' is an imaginary part of complex permittivity
The real and imaginary parts of the complex permittivity can be expressed as:
at ω R i C i <<1 and C 0 >>C i When the utility model is used, the water is discharged,
the complex dielectric constant can be expressed as
In the formula of r The relative dielectric constant of the cable insulation;
by
Wherein d is the thickness of the cable insulation; s is the area of cable insulation; sigma 0 Conductivity which is the insulation of the cable; the conductance loss based on the extended debye model can therefore be further expressed as:
the dielectric loss mainly comprises two parts of conductance loss and polarization loss, and on the basis of obtaining the conductance loss, the polarization loss part can be obtained by subtracting the conductance loss part from the whole dielectric loss of the cable. Thus, the polarization loss component is obtained by subtracting the conductance loss component from the overall dielectric loss:
in the extended Debye model, three polarization processes respectively correspond to respective branch parameters, and a dielectric loss expression corresponding to a third branch (a polarization loss part caused by a water tree defect) is as follows:
derivation of the expression for the third branch:
the frequency corresponding to the extreme value is:
therefore, the frequency corresponding to the loss peak of the polarization loss of the third branch of the cable sample can be rapidly obtained.
tanδ p3 Does not always exceed tan delta of another sample in all frequency ranges after being connected to the graph p3 To obtain tan delta p3 The peak value of (A) can be directly seen, and the tan delta of the cables with similar models can be visually seen p3 The frequencies corresponding to the peak values are very close, so the comparison peak value should be compared near the peak frequency, the derivation process is only a specific basis for explaining the operation, and the actual measurement can be directly substituted according to the obtained formula.
The polarization loss tan delta caused by water tree defects in the step (3) p3 The relationship between the magnitude of (a) and the cable aging is: said polarization loss tan delta around the peak frequency p3 The larger the value of (A), the more the cable water tree deteriorates.
According to the method, the time domain parameters of the polarization current are quickly converted into corresponding frequency domain information by using the extended Debye model, the polarization loss and the conductance loss of the dielectric loss of the cable are effectively distinguished, and the polarization loss caused by the water tree defect is extracted. Calculated in the cable insulation materialPolarization losses (tan delta) due to water tree defects p3 ) The size of the peak value is used for diagnosis, so that the measurement time of the polarization current is shortened to a great extent, the diagnosis time is shortened, and the aging condition of the cable can be accurately reflected.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and any modification, equivalent replacement, or improvement made within the spirit and scope of the present invention should be included.
Claims (2)
1. The method for quickly diagnosing the loss decoupling of the insulating low-frequency medium of the crosslinked polyethylene cable is characterized by comprising the following steps of: the method comprises the following steps:
(1) firstly, measuring the polarization current value of the cable;
(2) then, performing time-frequency domain conversion by expanding a Debye model, rapidly converting the measured polarization current value into a dielectric parameter under a corresponding frequency domain, and obtaining an integral dielectric loss factor tan delta of the XLPE cable insulation;
(3) on the basis, the integral dielectric loss factor is split to obtain the conductance loss and the polarization loss, and the polarization loss tan delta caused by the water tree defect is extracted by expanding the polarization branch caused by the water tree defect represented on the Debye model p3 ；
(4) By comparison of tan delta around the peak frequency p3 Judging the aging state of the cable according to the value;
the specific method of the step (2) comprises the following steps:
respectively representing different types of polarization processes by using a plurality of resistance-capacitance series branches by using an extended Debye model; three branches in the extended Debye model respectively represent three polarization processes contained in the insulation of the equivalent XLPE cable, and in the third-order model, C 0 Represents the cable insulator capacitance; r is 0 Representing a cable leakage resistance; r 1 、C 1 The branch parameters are used for representing the polarization of the cable insulating material body; r 2 、C 2 Is a parameter representing a branch circuit for representing the polarization of an amorphous and crystal interface; r 3 、C 3 To express the polarization branch parameters caused by characterizing the defects of the water treeCounting;
the complex capacitance C (ω) can be calculated by extending the three branches in the Debye model:
c represents complex capacitance, C 'represents the real part of the complex capacitance, C' represents the imaginary part of the complex capacitance, j is an imaginary unit,
the integral dielectric loss factor can be obtained according to the ratio of the imaginary part and the real part of the complex capacitor:
in the step (3), the whole dielectric loss is split to obtain a polarization loss part, and a conductance loss expression is obtained firstly based on a decoupling method of an extended Debye model:
when a sinusoidal voltage U (ω) is applied to the insulation, the current flowing through the insulation of the cable can be expressed as:
I(ω)＝jω[C'(ω)-jC”(ω)]U(ω)
＝jωC a [ε'(ω)-jε”(ω)]U(ω)
in the formula C a The capacitor is a vacuum geometric capacitor of cable insulation, U (omega) is sinusoidal voltage, I (omega) is sinusoidal current, j is an imaginary number unit, omega is angular frequency, C 'is a real part of complex capacitance, C' is an imaginary part of complex capacitance, epsilon 'is a real part of complex dielectric constant, and epsilon' is an imaginary part of complex dielectric constant;
the real and imaginary parts of the complex permittivity can be expressed as:
at ω R i C i <<1 and C 0 >>C i When the temperature of the water is higher than the set temperature,
the complex dielectric constant can be expressed as
In the formula epsilon r The relative dielectric constant of the cable insulation;
by
Wherein d is the thickness of the cable insulation; s is the area of cable insulation; sigma 0 Conductivity which is the insulation of the cable; vacuum geometric capacitor C for cable insulation a And a leakage resistance R 0 Can be represented by the actual parameters of the cable as:
wherein a and b are the radius of the inner and outer conductors of the cable; l is the cable length; sigma 0 Conductivity for cable insulation
The conductance loss based on the extended debye model can therefore be further expressed as:
the polarization loss part is the integral dielectric loss factor of the cable insulation minus the conductance loss part,
the overall dielectric loss factor of the cable insulation can be expressed as:
2. the method for rapidly diagnosing dielectric loss decoupling of low frequency of cross-linked polyethylene cable insulation according to claim 1, wherein in step (4), the polarization loss tan δ caused by water tree defect p3 The relationship between the size of (2) and the aging state of the cable water tree is as follows: said polarization loss tan delta around the peak frequency p3 The larger the value of (A), the larger theThe more the cable water tree ages.
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