CN107765148A - A kind of method that the distribution of insulating materials trap level is calculated based on pulse electroacoustic method - Google Patents

A kind of method that the distribution of insulating materials trap level is calculated based on pulse electroacoustic method Download PDF

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CN107765148A
CN107765148A CN201710948278.5A CN201710948278A CN107765148A CN 107765148 A CN107765148 A CN 107765148A CN 201710948278 A CN201710948278 A CN 201710948278A CN 107765148 A CN107765148 A CN 107765148A
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mrow
msub
mfrac
slow
trap
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CN107765148B (en
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郝建
廖瑞金
杨丽君
李剑
成立
赵学童
袁媛
邹润豪
陈光辉
吴高林
王谦
李小平
张施令
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Chongqing University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/12—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

Abstract

The present invention relates to a kind of method that the distribution of insulating materials trap level is calculated based on pulse electroacoustic method, belong to the electric property representational field of insulating materials.This method dissipates according to space charge has the characteristics of speed, first, proposing to carry out space charge that is quick and dissipating at a slow speed respectively the exponential fitting analysis method of charge decay rule, Traditional Space electric charge is improved to second-order dynamic relational expression of the space charge with resolution time with the single order Kinetic model for substrate of resolution time；Second, fast, slow electric charge initial decay density and damping time constant in the second-order dynamic relational expression based on acquisition, by it is improved have to distinguish the calculation formula that deep, shallow trapping state is distributed and obtain deep, shallow trap energy level corresponding to fast, slow electric charge respectively be distributed, and then realize that the reason for judgement causes depth, shallow trapping state distribution to change belongs to physical imperfection or chemical imperfection.

Description

A kind of method that the distribution of insulating materials trap level is calculated based on pulse electroacoustic method
Technical field
The invention belongs to the electric property representational field of insulating materials, is related to a kind of based on pulse electroacoustic method calculating insulation material Expect the method for trap level distribution.
Background technology
The space charge of insulating materials accumulated inside is insulated from that performance is closely related, and space charge can cause in medium The distortion of portion's Electric Field Distribution, internal field is played a part of weakening or strengthened, if electric field distortion is serious, insulating materials will be caused Breakdown and aging, directly affect the reliability and security of insulation system.Space charge and the distribution of traps in dielectric It is closely related, it is accurate to calculate the distribution of insulating materials trap level, Material Physics defect and chemical imperfection are distinguished, is to grasp insulation material Expect the key of performance.
1) trap level distribution character is grasped to understanding that space charge behavior is particularly important
A. the main source of space charge
Due to reasons such as manufacturing process, there is small physical imperfection or impurity etc. inside the dielectric produced. Due to extra electric field and the influence of polarization, the potential barrier of electronics or hole effusion electrode reduces, electronics or hole from electrode emission Migration is produced in the presence of extra electric field, the trap formed in transition process by impurity in medium captures and turns into sky Between electric charge.
B. harm of the space charge to insulating properties
Space charge effect is to influence the principal element of dielectric substance dielectric strength.It is defeated for operating direct current Transformer (converter power transformer, direct current cables), because of the long term of DC electric field component, oil-immersed insulating paper or cable polyethylene Material internal can produce space charge injection phenomenon.The electric charge of injection will be transported in material bodies, accumulated, be dissipated, these Process Space-charge will all weaken internal field in external electrical field and intensive aspect, and field strength distribution distortion shadow is produced in dielectric Ring, cause getting up early insulation harm, accelerate the aging of dielectric, can cause conduction current increase, shelf depreciation etc. existing when serious As, cause equipment damage or even fail, the safe operation of serious threat equipment.Particularly direct current power equipment is carrying out reversed polarity During operation, the electric field distortion as caused by space charge is easier to cause the damage of insulation, induces insulation fault and influences equipment just Often operation.
C. grasp trap level is distributed the importance to understanding insulating materials space charge behavior
Space charge injection, transport to insulating materials, accumulation, attenuation characteristic are studied, it is possible to understand that insulating materials The transport property and mechanism of internal space-charge, help to study space charge in dielectric aging and insulation harm behavior Role and influence, so that the relation between more deep understanding material physical chemistry microstructure and electric property, In order to improve the insulating properties of insulating materials, to lift the thermal stability of insulating materials and extending power equipment service life Reference frame is provided.
Space charge and the distribution of traps in dielectric are closely related.In the evanishment of space charge, due to falling into Electric-charge-dissipating (detrapping) speed in trap is different, and some can dissipate after pressure is gone in 10 minutes, and some needs a few hours could Dissipate, therefore, it is determined that the energy level of trap is different, and trap is divided into deep trap and the class of shallow trap two.Space charge in deep trap What is dissipated is fast, and the electric-charge-dissipating in shallow trap is fast.The generation of trap is mainly determined by the defects of insulating materials.Insulation material The defects of material can be divided into physical imperfection and chemical imperfection.Had due to production technology, inside insulating materials small Physical imperfection, and as the aging of insulating materials, the destruction of microstructure can produce new physical imperfection again.Simultaneously in aging Chain rupture, generation occur for Cheng Zhong, the chemical substance (cellulose in such as paper oil insulation, the polyethylene in LDPE materials) of insulating materials New small-molecule substance, produce chemical imperfection.Due to depth, shallow trap energy level distribution and density and dielectric it is hollow between electricity Aggregation, migration, the dissipation behavior of lotus are closely coupled, therefore, accurate to calculate the distribution of insulating materials trap level, distinguish Material Physics Defect and chemical imperfection, it is the key for grasping insulating material properties.
2) conventional method of insulating materials trap level distribution is calculated
The method for being commonly used to analyze the distribution of insulating materials trap level mainly has two kinds, first, thermally stimulated current method；Two It is the trap level distribution calculation method based on pulse electroacoustic method.
A. thermally stimulated current (TSC) method
Thermostimulation theory grows up on the basis of medium physics, this theoretical method it is fairly simple practical and And and can accurately measures the micro-parameter of Cucumber (such as dielectric, insulating materials, semiconductor, electret).Heat Stimulating current method be one in face of material warms one side measure.Due to charged particle micro-parameter (such as activation energy in material H, slack time τ etc.) it is different, it is easy for separating the charged particle of the various different H or τ in material with thermostimulation method, So as to obtain respective parameter.
Thermally stimulated current method is a kind of heat analysis method.First apply DC voltage to sample at a certain temperature, make sample Polarization；In the case of pressurization, sample is cooled to a low temperature to freeze electric charge rapidly；Then polarizing voltage, sample are removed Short-circuit certain time is to eliminate the influence of spuious electric charge.Last linear temperature increase, the short circuit current of external circuit is measured, the electric current and temperature The curve of degree is thermally stimulated current curve.
According to TSC curves, there is the theoretical formula that simplifies of following most basic thermally stimulated current to can determine that trap parameters
B is dynamics series；N is the number corresponding to t (or during temperature T) medium trapped electron；E is that trap is deep Degree；T is kelvin rating；K is Boltzmann constant；S is frequency factor；n0For corresponding to the initial moment (or minimum temperature) Trap number.
Thermally stimulated current method can go out the property and polarity in the source of electric current, i.e. carrier in medium respectively, and this is heat One of the advantages of stimulating current method.But because this method needs to cool to sample and heated, have to sample and destroy Property.
B. traditional trap level distribution calculation method based on pulse electroacoustic method
Pulse electroacoustic method is widely used for measuring the space charge characteristic of solid dielectric.In brief, its principle is The Coulomb force as caused by external pulse electric field causes the concussion of media interior electric charge to produce acoustical signal, and the acoustical signal ripple is by outside Piezoelectric transducer receives and is translated into electric signal, can be drawn after signal and mathematical method processing in dielectric Portion's distribution of charges situation.
Traditional trap computational methods based on pulse electroacoustic method are specific as follows
After extra electric field is removed, the sunken electric charge that enters in insulating materials is reduced with the increase of time, and the phenomenon is referred to as Electric charge detrapping.The change of charge density (potential decay) in trap can be approximated to be exponential damping law, as shown in formula (2)：
σ=Ae-t/τ (2)
σ is surface charge density, and A is initial surface charge density, and τ is charge dissipation time constant, and t is to disappear into sunken electric charge Dissipate the time.
The current density change rule containing damping time constant can be further obtained, as shown in formula (3)：
| j (t) | it is current density, r ' is mean charge dapths, is 120pm.L is thickness of sample.
Enter sunken carrier by shallow trap after applied voltage removes, in dielectric first to discharge, in deep trap Discharged after carrier, the carrier release current decayed at different temperatures with the time reflects the trap energy fraction of specimen surface Cloth rule.Trap level E can be drawntAnd current density j and trap density NtRelation：
Et=KTln (ν t) (4)
V is electronic vibration frequency 3 × 1012s-1, K is Boltzmann constant 8.568 × 10-5EV/K, T are that absolute temperature (is opened Family name's temperature).f0(Et) it is that initial occupation rate -1/2, e of trap in medium is electron charge 1.6 × 10-19C。
Ifη 1 and η 2 is all constant.Then
It can be seen that trap level density N (Et) closely related with the damping time constant of charge density and die-away time.
Trap level distribution calculation method based on pulse electroacoustic method, it is to obtain space charge with going to press the time to decline first Subtract rule, obtain the initial decay density and decay attenuation constant of space charge；Then according to parameter is obtained, according to formula (3-6) Calculate the trap level distribution of insulating materials.When existing method only obtains the damping time constant of an exponential law, so as to will Trap level unification, it can not accurately show deep, shallow two kinds of traps inside insulating materials be present, while also can not be to causing The reason for deep, shallow trap energy and distribution character change carries out accurate judgement.
The content of the invention
In view of this, insulating materials trap energy fraction is calculated based on pulse electroacoustic method it is an object of the invention to provide one kind The method of cloth, for insufficient existing for existing insulating materials trap level distribution measuring and computational methods：First, thermally stimulated current It is owned by France in damage test；Second, trap computational methods of the tradition based on pulse electroacoustic method obtain the space charge of an exponential law Damping time constant, trap level is distributed unification, can not accurately show to fall into the presence of deep, shallow two kinds inside insulating materials Trap, at the same also can not be to causing depth, shallow trap energy and distribution character to change the reason for carry out accurate judgement；Realize insulating materials Deep, shallow trapping state distribution and its calculating of level density distribution, realize again and judge to cause depth, shallow trapping state distribution to change Reason belongs to physical imperfection or chemical imperfection.
To reach above-mentioned purpose, the present invention provides following technical scheme：
A kind of method that the distribution of insulating materials trap level is calculated based on pulse electroacoustic method, is comprised the following steps：
S1：The space charge dissipation behavior of insulating materials is obtained with electroacoustic pulse interval charge measurement method；
S2：Obtain space charge amount corresponding to different resolution times；
S3：The analysis of second-order dynamic exponential fitting is carried out to space charge attenuation characteristic, is obtained comprising quick and empty at a slow speed Between electric-charge-dissipating rule second-order dynamic exponentially fitted formulae；
S4：The calculation formula being distributed according to proposing to distinguish deep, shallow trapping state, calculate obtain corresponding to fast, slow electric charge it is deep, The energy level distribution of shallow trap；
S5：According to depth, the energy level distribution character of shallow trap, defect type is judged.
Further, in step s3, the specific fitting formula of the second-order dynamic exponential fitting analysis is
In formula, σfastWith σslowThe respectively fast electric charge in surface, i.e., electric charge and the slow electric charge in surface in shallow trap, i.e., in deep trap Electric charge；AfastWith AslowThe respectively fast electric charge initial density in surface and the slow electric charge initial density in surface；τfastWith τslowIt is respectively fast The charge dissipation time constant of electric charge and slow electric charge；|jfast(t) | with | jslow(t) | it is respectively the electric current of fast electric charge and slow electric charge Density；| j (t) | it is current density；R' is mean charge dapths；L is thickness of sample；T is into sunken charge dissipation time.
Further, the step S4 is specially：
In formula, e is electron charge 1.6 × 10-19C；K is Boltzmann constant 8.568 × 10-5eV/K；T is absolute temperature； f0(Et-fast) and f0(Et-slow) be respectively shallow trap and deep trap initial occupation rate；N(Et-fast) it is fast electric charge difference energy level Trap density, N (Et-slow) be slow electric charge difference energy level trap density；η1-fastWith η1-slowIt is all constant；η2-fastWith η2-slowIt is all constant Et-fastWith Et-slowThe trap level of respectively fast electric charge and slow electric charge, Et-fast=KTln (ν t), Et-slow =KTln (ν t)；V is electronic vibration frequency 3 × 1012s-1。
Further, the step S5 is specially：
The deep trap level density of insulating materials is bigger, is more partial to chemical imperfection；The deep trap energy level of insulating materials is close Spend smaller, be more partial to physical imperfection.
The beneficial effects of the present invention are：
(1) exponential fitting point by carrying out charge decay rule respectively to space charge that is quick and dissipating at a slow speed is proposed Analysis, second-order dynamic of the space charge with resolution time is improved to by Traditional Space electric charge with the single order kinetics equation of resolution time Learn equation；
(2) propose to distinguish the calculation formula that deep, shallow trapping state is distributed, according to fast in second-order dynamic relational expression, slow electricity Lotus initial decay density and damping time constant, calculate and obtain deep, shallow trap energy level distribution corresponding to fast, slow electric charge, realize The reason for judgement causes depth, shallow trapping state distribution to change belongs to physical imperfection or chemical imperfection.
Brief description of the drawings
In order that the purpose of the present invention, technical scheme and beneficial effect are clearer, the present invention provides drawings described below and carried out Explanation：
Fig. 1 is flow chart of the present invention；
Fig. 2 (a) is space charge dissipation characteristic of the new paper oil insulation medium (fresh oil+new insulating paper) under different field strength； Fig. 2 (b) is space charge dissipation characteristic of the aging paper oil insulation medium (ageing oil+new insulating paper) under different field strength；
Fig. 3 (a) is that space charge dissipation characteristic of the new paper oil insulation medium (fresh oil+new insulating paper) under different field strength is intended Close analysis；Fig. 3 (b) is that space charge dissipation of the aging paper oil insulation medium (ageing oil+new insulating paper) under different field strength is special Property Fitting Analysis；
Fig. 4 (a) is the traditional trap result of calculation based on pulse electroacoustic method of new paper oil insulation medium (fresh oil+new insulating paper)；
Fig. 4 (b) is that trap of aging paper oil insulation medium (ageing oil+new insulating paper) tradition based on pulse electroacoustic method calculates As a result；
Fig. 5 (a) is space charge dissipation characteristic of the new paper oil insulation medium (fresh oil+new insulating paper) under different field strength； Fig. 5 (b) is space charge dissipation characteristic of the aging paper oil insulation medium (ageing oil+new insulating paper) under different field strength；
Fig. 6 (a) is that space charge dissipation characteristic of the new paper oil insulation medium (fresh oil+new insulating paper) under different field strength is intended Close and divide；Fig. 6 (b) is space charge dissipation characteristic of the aging paper oil insulation medium (ageing oil+new insulating paper) under different field strength Fitting Analysis；
Fig. 7 (a) is based on pulse electroacoustic method insulating materials trap for new paper oil insulation medium (fresh oil+new insulating paper) is improved The result of calculation of energy level distribution；Fig. 7 (b) is based on electroacoustic arteries and veins for aging paper oil insulation medium (ageing oil+new insulating paper) is improved Rush the result of calculation of method insulating materials trap level distribution.
Embodiment
Below in conjunction with accompanying drawing, the preferred embodiments of the present invention are described in detail.
Fig. 1 is flow chart of the present invention.The first step：The sky of insulating materials is obtained with electroacoustic pulse interval charge measurement method Between electric-charge-dissipating behavior；Second step：Obtain space charge amount corresponding to different resolution times；3rd step：Space charge is decayed Characteristic carries out the analysis of second-order dynamic exponential fitting, obtains comprising quick and space charge dissipation law at a slow speed second-order dynamic Exponentially fitted formulae；4th step：The calculation formula of deep shallow trapping state distribution is distinguished according to proposition, calculates fast, the slow electric charge of acquisition The energy level distribution of corresponding depth, shallow trap；5th step：According to depth, the energy level distribution character of shallow trap, defect type is judged.
After removing voltage, some dissipates in the short period of time for electric charge in medium, and another part electric charge needs very The long time is dissipated, therefore the trap in medium is divided into shallow trap and the class of deep trap two；The electric-charge-dissipating block of shallow trap, gets deeply stuck in Electric-charge-dissipating in trap is slow.Therefore, first, above-mentioned shown single order kinetics equation is improved into second-order dynamic equation first, Second, propose to distinguish the calculation formula of deep shallow trapping state distribution.Improvement specific steps to conventional first order kinetics equation are such as Shown in table 1：
The improved New calculating method based on the distribution of pulse electroacoustic method insulating materials trap level of table 1
By taking oil-immersed insulating paper as an example, carry out the specific of implementation process of the present invention and tell about：
First, traditional trap level distribution calculation method based on pulse electroacoustic method
1) new paper oil insulation medium (fresh oil+new insulating paper) and aging paper oil insulation medium (ageing oil+new insulation are surveyed Paper) the space charge dissipation characteristic under different field strength it is as follows：
Fig. 2 is new paper oil insulation medium (fresh oil+new insulating paper) and aging paper oil insulation medium (ageing oil+new insulating paper) The space charge dissipation characteristic under different field strength.
2) to new paper oil insulation medium (fresh oil+new insulating paper) under different field strength and aging paper oil insulation medium (ageing oil+ New insulating paper) space charge dissipation law carry out single order kinetic index Fitting Analysis, matched curve (discrete point be actual measurement Value, solid line is matched curve) and specifically fitting formula is as follows：
Fig. 3 is using traditional trap computational methods based on pulse electroacoustic method, new paper oil insulation medium (fresh oil+new insulation Paper) and aging paper oil insulation medium (ageing oil+new insulating paper) the space charge dissipation property fitting under different field strength point Analysis.
The traditional trap computational methods space charge dissipation single order kinetic index fitting formula based on pulse electroacoustic method of table 2
3) according to fit equation, the parameter of charge decay initial density and damping time constant is extracted, calculates trap level Distribution, it is as a result as follows：
Et=KTln (ν t) (4)
Fig. 4 is traditional trap result of calculation based on pulse electroacoustic method.
4) it is visible by above-mentioned trap level distribution results, utilize single order kinetics equation only one damping time constant meter The trap level distribution only one peak of calculation, is the equalization reflection of depth trap, therefore cannot be distinguished by deep trap or shallow fall into Trap.
2nd, the improved new method that the distribution of insulating materials trap level is calculated based on pulse electroacoustic method
1) new paper oil insulation medium (fresh oil+new insulating paper) and aging paper oil insulation medium (ageing oil+new insulation are surveyed Paper) the space charge dissipation characteristic under different field strength it is as follows：
Fig. 5 is new paper oil insulation medium (fresh oil+new insulating paper) and aging paper oil insulation medium (ageing oil+new insulating paper) The space charge dissipation characteristic under different field strength.
2) to new paper oil insulation medium (fresh oil+new insulating paper) under different field strength and aging paper oil insulation medium (ageing oil+ New insulating paper) space charge dissipation law carry out the analysis of second-order dynamic exponential fitting, obtain quick with sky that is dissipating at a slow speed Between electric charge attenuation law, matched curve (discrete point is measured value, and solid line is matched curve) and specific fitting formula are as follows：
Fig. 6 is using the improved New calculating method based on the distribution of pulse electroacoustic method insulating materials trap level, new oilpaper The sky under different field strength of dielectric (fresh oil+new insulating paper) and aging paper oil insulation medium (ageing oil+new insulating paper) Between charge dissipation characteristics Fitting Analysis.
Table 3：The improved New calculating method second-order dynamic based on the distribution of pulse electroacoustic method insulating materials trap level refers to Number fitting formula
As can be seen that compared with space charge dissipation single order dynamics approximating method of the tradition based on pulse electroacoustic method, two Rank kinetic index fitting analyzing method possesses more preferably fitting effect (fitting solid line and actual measurement discrete point in the electric-charge-dissipating later stage It coincide), the goodness of fit is higher than table 2 (traditional trap level distribution calculation method based on pulse electroacoustic method).
3) propose to distinguish the calculation formula that deep, shallow trapping state is distributed, according to fast, slow electric charge in second-order dynamic relational expression Initial decay density and damping time constant, calculate deep, shallow trap energy level distribution, realization corresponding to fast, the slow electric charge of acquisition and sentence Disconnected the reason for causing depth, shallow trapping state distribution to change, belongs to physical imperfection or chemical imperfection.It is specific as follows：
It can be seen that there is the calculation formula distinguished deep, shallow trapping state and be distributed by improved, fast, slow electric charge pair is obtained The energy level distribution of the depth answered, shallow trap.Space charge in deep trap dissipates fast, and the electric-charge-dissipating in shallow trap is fast. New paper oil insulation medium (fresh oil+new insulating paper) and aging paper oil insulation medium (ageing oil+new insulating paper) in comparison diagram 7 Deep, shallow trapping state partial results, it is seen then that the deep trap level density of aging paper oil insulation medium is noticeably greater than new paper oil insulation Medium, this is primarily due to caused by chemical imperfection caused by insulation oil degradation.Therefore, it is improved to be based on pulse electroacoustic method insulating materials The New calculating method of trap level distribution, it is achievable to judge that belonging to physics the reason for causing depth, shallow trapping state distribution to change lacks Fall into still chemical imperfection.
Finally illustrate, preferred embodiment above is merely illustrative of the technical solution of the present invention and unrestricted, although logical Cross above preferred embodiment the present invention is described in detail, it is to be understood by those skilled in the art that can be Various changes are made to it in form and in details, without departing from claims of the present invention limited range.

Claims (4)

  1. A kind of 1. method that the distribution of insulating materials trap level is calculated based on pulse electroacoustic method, it is characterised in that：This method includes Following steps：
    S1：The space charge dissipation behavior of insulating materials is obtained with electroacoustic pulse interval charge measurement method；
    S2：Obtain space charge amount corresponding to different resolution times；
    S3：Second-order dynamic exponential fitting is carried out to space charge attenuation characteristic to analyze, and is obtained comprising quickly and at a slow speed space is electric The second-order dynamic exponentially fitted formulae of lotus dissipation law；
    S4：The calculation formula of deep shallow trapping state distribution is distinguished according to proposition, calculates deep, shallow corresponding to fast, the slow electric charge of acquisition fall into The energy level distribution of trap；
    S5：According to depth, the energy level distribution character of shallow trap, defect type is judged.
  2. 2. a kind of method that the distribution of insulating materials trap level is calculated based on pulse electroacoustic method according to claim 1, its It is characterised by：In step s3, the specific fitting formula of the second-order dynamic exponential fitting analysis is
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    In formula, σfastWith σslowThe respectively fast electric charge in surface, i.e., electric charge and the slow electric charge in surface, i.e. electric charge in deep trap in shallow trap； AfastWith AslowThe respectively fast electric charge initial density in surface and the slow electric charge initial density in surface；τfastWith τslowRespectively fast electric charge With the charge dissipation time constant of slow electric charge；|jfast(t) | with | jslow(t) | it is respectively the current density of fast electric charge and slow electric charge； | j (t) | it is current density；R' is mean charge dapths；L is thickness of sample；T is into sunken charge dissipation time.
  3. 3. a kind of method that the distribution of insulating materials trap level is calculated based on pulse electroacoustic method according to claim 2, its It is characterised by：The step S4 is specially：
    <mrow> <mo>|</mo> <mi>j</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>=</mo> <mo>|</mo> <msub> <mi>j</mi> <mrow> <mi>f</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>j</mi> <mrow> <mi>s</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> <mo>|</mo> <mo>=</mo> <mfrac> <mrow> <mi>e</mi> <mi>L</mi> <mi>K</mi> <mi>T</mi> </mrow> <mrow> <mn>2</mn> <mi>t</mi> </mrow> </mfrac> <msub> <mi>f</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mrow> <mi>t</mi> <mo>-</mo> <mi>f</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mrow> <mi>t</mi> <mo>-</mo> <mi>f</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mi>e</mi> <mi>L</mi> <mi>K</mi> <mi>T</mi> </mrow> <mrow> <mn>2</mn> <mi>t</mi> </mrow> </mfrac> <msub> <mi>f</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mrow> <mi>t</mi> <mo>-</mo> <mi>s</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mrow> <mi>t</mi> <mo>-</mo> <mi>s</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>&amp;eta;</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>f</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>e</mi> <mi>L</mi> <mi>K</mi> <mi>T</mi> </mrow> <mn>2</mn> </mfrac> <msub> <mi>f</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mrow> <mi>t</mi> <mo>-</mo> <mi>f</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>&amp;eta;</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>s</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>e</mi> <mi>L</mi> <mi>K</mi> <mi>T</mi> </mrow> <mn>2</mn> </mfrac> <msub> <mi>f</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mrow> <mi>t</mi> <mo>-</mo> <mi>s</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>&amp;eta;</mi> <mrow> <mn>2</mn> <mo>-</mo> <mi>f</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <mi>r</mi> <mo>&amp;prime;</mo> </msup> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mrow> <mi>L</mi> </mfrac> <mo>,</mo> <msub> <mi>&amp;eta;</mi> <mrow> <mn>2</mn> <mo>-</mo> <mi>s</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <mi>r</mi> <mo>&amp;prime;</mo> </msup> <msub> <mi>A</mi> <mrow> <mi>s</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mrow> <mi>L</mi> </mfrac> </mrow>
    <mrow> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mrow> <mi>t</mi> <mo>-</mo> <mi>f</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msub> <mi>&amp;eta;</mi> <mrow> <mn>2</mn> <mo>-</mo> <mi>f</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <msub> <mi>&amp;eta;</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>f</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mfrac> <mfrac> <mi>t</mi> <msub> <mi>&amp;tau;</mi> <mrow> <mi>f</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mfrac> <msup> <mi>e</mi> <mfrac> <mrow> <mo>-</mo> <mi>t</mi> </mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>f</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mfrac> </msup> <mo>,</mo> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mrow> <mi>t</mi> <mo>-</mo> <mi>s</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msub> <mi>&amp;eta;</mi> <mrow> <mn>2</mn> <mo>-</mo> <mi>s</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> <msub> <mi>&amp;eta;</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>s</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mfrac> <mfrac> <mi>t</mi> <msub> <mi>&amp;tau;</mi> <mrow> <mi>s</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mfrac> <msup> <mi>e</mi> <mfrac> <mrow> <mo>-</mo> <mi>t</mi> </mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>s</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mfrac> </msup> </mrow>
    In formula, e is electron charge 1.6 × 10-19C；K is Boltzmann constant 8.568 × 10-5eV/K；T is absolute temperature；f0 (Et-fast) and f0(Et-slow) be respectively shallow trap and deep trap initial occupation rate；N(Et-fast) it is fast electric charge difference energy level Trap density, N (Et-slow) be slow electric charge difference energy level trap density；η1-fastWith η1-slowIt is all constant；η2-fastWith η2-slow It is all constant Et-fastWith Et-slowThe trap level of respectively fast electric charge and slow electric charge, Et-fast=KTln (ν t), Et-slow=KT ln(νt)；V is electronic vibration frequency 3 × 1012s-1。
  4. 4. a kind of method that the distribution of insulating materials trap level is calculated based on pulse electroacoustic method according to claim 1, its It is characterised by：The step S5 is specially：
    The deep trap level density of insulating materials is bigger, is more partial to chemical imperfection；The deep trap level density of insulating materials is got over It is small, more it is partial to physical imperfection.
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CN116106657A (en) * 2022-11-18 2023-05-12 西南交通大学 Method for evaluating ageing state of EPDM (ethylene-propylene-diene monomer) cable based on electron trap effect

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