A method for calculating the breakdown field strength of cable insulation of different thicknesses at different temperatures.

Abstract

This invention discloses a method for calculating the breakdown field strength of cable insulation of different thicknesses at different temperatures. The method includes the following steps: conducting surface potential decay experiments on XLPE samples of different thicknesses to obtain surface potential decay curves; obtaining trap parameters for XLPE samples of different thicknesses based on the surface potential decay curves; substituting the trap parameters into a bipolar carrier model to calculate the change in electron energy inside the XLPE sample with the applied pressure time; determining that the XLPE sample has broken down when the electron energy is greater than the trap energy level calculated from the surface potential decay experiment; recording the DC breakdown field strength of XLPE samples of different thicknesses at different temperatures to construct a DC breakdown field strength prediction model for XLPE samples. This invention can accurately evaluate the DC breakdown field strength of various types of XLPE samples, has the advantages of convenient operation and high universality, and shows high accuracy compared with actual experiments.

Description

Technical Field

[0001] This invention relates to the field of high voltage and insulation technology, specifically a method for calculating the breakdown field strength of cable insulation of different thicknesses at different temperatures. Background Technology

[0002] With the increasing scarcity of near-shore wind farm sites and the continuous increase in the distance between offshore wind farms and shore, the development of high-capacity, long-distance AC submarine cable systems has become an urgent priority. Cross-linked polyethylene (XLPE) is widely used in submarine cables of different voltage levels due to its superior electrical, thermal, and mechanical properties. However, increasing the current carrying capacity of submarine cables will cause the conductor temperature to rise, leading to thermal aging of the XLPE insulation and a decline in insulation performance, which may even cause breakdown accidents in severe cases. To ensure the reliable operation of submarine cables, a relatively conservative thickness design is usually chosen, which significantly increases production costs, and the insulation performance, such as breakdown voltage, may not be effectively improved at high temperatures. Therefore, studying the impact of insulation thickness and operating temperature on the dielectric properties of XLPE insulation in submarine cables is of great significance for the development of ultra-high voltage submarine cables.

[0003] As operating temperature increases, the activity of the molecular chains within the XLPE sample increases, which is more conducive to carrier migration and thus leads to sample breakdown. As the thickness of the XLPE sample increases, the number of local defects within the sample also increases, making the sample more prone to breakdown. Therefore, temperature and thickness are key factors affecting the breakdown field strength of XLPE samples. However, currently, there is a lack of computational models for the breakdown field strength of XLPE samples based on temperature and thickness variations. Assessing the breakdown field strength of XLPE samples typically requires repeated experiments, which is extremely resource-intensive as the variety of XLPE samples increases. Therefore, there is an urgent need for an effective and feasible method to directly establish breakdown models for XLPE samples of different thicknesses at different temperatures, enabling direct calculation and prediction of the breakdown field strength of XLPE samples of different thicknesses under different testing conditions. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the breakdown field strength of cable insulation of different thicknesses at different temperatures. This invention can accurately evaluate the DC breakdown field strength of various XLPE samples and has the advantages of convenient operation and wide applicability.

[0005] The technical solution of this invention: a method for calculating the breakdown field strength of cable insulation of different thicknesses at different temperatures, comprising the following steps:

[0006] Step 1: Conduct surface potential decay experiments on XLPE samples of different thicknesses to obtain surface potential decay curves of XLPE samples;

[0007] Step 2: Obtain the trap parameters of XLPE samples with different thicknesses based on the surface potential decay curves of XLPE samples with different thicknesses. Substitute the trap parameters into the bipolar carrier model to calculate the change of the electronic energy inside the XLPE sample with the pressure time. When the electronic energy is greater than the trap energy level calculated by the surface potential decay experiment, the XLPE sample is determined to be broken down.

[0008] Step 3: Record the DC breakdown field strength of XLPE samples of different thicknesses at different temperatures, and construct a DC breakdown field strength prediction model for XLPE samples.

[0009] Step 4: Based on the thickness and operating temperature of any XLPE sample to be tested, calculate the DC breakdown field strength of the XLPE sample to be tested using the DC breakdown field strength prediction model.

[0010] The above-mentioned calculation method for the breakdown field strength of cable insulation of different thicknesses at different temperatures, in step 1, the preparation of the XLPE samples of different thicknesses is as follows: XLPE granules of mass m are uniformly placed in a mold of area S using a flat plate hot pressing method. The mold is then placed in a flat plate vulcanizing machine for high-temperature and high-pressure vulcanization. After complete vulcanization, the mold and XLPE samples are removed. The mass m of the XLPE granules satisfies the functional relationship shown in formula (1):

[0011] m=ρ·d; (1)

[0012] Where ρ is the density of XLPE granules; d is the thickness of the XLPE sample.

[0013] The aforementioned method for calculating the breakdown field strength of cable insulation of different thicknesses at different temperatures involves, after obtaining the XLPE sample, using a thickness gauge with an accuracy of at least 0.01 mm to measure the thickness at at least 5 different locations on the XLPE sample, and calculating the average thickness of the XLPE sample according to formula (2).

[0014]

[0015] Where d XLPE d represents the average thickness of the XLPE pattern. i The thickness of the XLPE sample obtained from the i-th measurement is denoted as ; i represents the number of measurements, i = 1, 2, 3...N; and N represents the total number of measurements performed.

[0016] In the aforementioned method for calculating the breakdown field strength of cable insulation of different thicknesses at different temperatures, step 1, the surface potential decay experiment on the XLPE sample, must meet the following conditions:

[0017] 1) The XLPE sample is placed completely flat on the ground electrode, and the distance between the equalizing grid and the XLPE sample to be tested, and between the equalizing grid and the needle electrode is kept constant; the ambient temperature and humidity remain constant during the test.

[0018] 2) The ground electrode is heated by a thermocouple, and the temperature of the XLPE sample is detected by a temperature sensor. The surface potential decay measurement is started after the XLPE sample is stable at the test temperature for 5-7 minutes. The measurement is performed at at least four different temperatures for each thickness of XLPE sample.

[0019] 3) The voltage applied to the needle electrode is -8kV, the voltage applied to the equalizing grid is -4kV, and the charging time is 3-5min. After charging, the XLPE sample should be moved to the potentiometer within 3-5s to record the decay of the surface potential. The recording time is 35-45min.

[0020] In the aforementioned method for calculating the breakdown field strength of cable insulation of different thicknesses at different temperatures, step 2, the step of obtaining the trap parameters of XLPE samples of different thicknesses based on the surface potential decay curves of XLPE samples of different thicknesses, is as follows:

[0021] First, the surface potential decay curve is fitted using a double natural exponential function, and the fitting formula is shown in formula (3):

[0022]

[0023] Where V(t) represents the decay of the surface potential of the XLPE sample over time; A, B, t1, and t2 are all fitting constants; and t is the test time.

[0024] Next, the trap energy level distribution of XLPE samples with different thicknesses was obtained based on the test time and test temperature. The calculation process is shown in formula (4):

[0025]

[0026] Among them, E T For the trap energy level; k B is Boltzmann constant; T is the test temperature; h is Planck's constant; v is the vibrational frequency of molecules inside the XLPE sample;

[0027] Then, based on the surface potential decay curve obtained by fitting formula (3) over time, the trap charge density of XLPE samples with different thicknesses is obtained by differentiation as shown in formula (5):

[0028]

[0029] Among them, Q s(t) represents the trap charge density; ε0 represents the vacuum permittivity; ε r V is the relative permittivity; V(t) represents the decay of the surface potential of the XLPE sample over time; q e The amount of charge per unit charge;

[0030] Based on formulas (4) and (5), the trapping parameters of XLPE samples with different thicknesses can be obtained.

[0031] The aforementioned method for calculating the breakdown field strength of cable insulation of different thicknesses at different temperatures, by substituting the trap parameters into the bipolar carrier model, calculates the change of electron energy inside the XLPE sample with the time of pressurization as follows:

[0032] A bipolar carrier model for XLPE samples of different thicknesses is introduced to simulate the migration of carriers inside XLPE samples of different thicknesses, as shown in Equation (6):

[0033]

[0034] In this context, the subscript 'a' represents different types of charge carriers, specifically free electrons (eμ), trapped electrons (et), free holes (hμ), and trapped holes (ht); j a (r,z,t) represents the magnitude of the current density of carrier a at time t in the r,z coordinate system; μ a n is the mobility of carrier a; a (r,z,t) represents the charge density of carrier a at time t in the r,z coordinate system; D fa ρ(r,z,t) is the decongestion coefficient; E(r,z,t) is the electric field intensity at time t in the r,z coordinate system; ρ(r,z,t) is the volume charge density at time t in the r,z coordinate system; ε is the dielectric constant of the XLPE sample; s a (r,z,t) represents the interaction reaction of different charge carriers at time t in the r,z coordinate system, and is called the source phase. Its calculation method is shown in formula (7):

[0035]

[0036] Where s a B is the composite coefficient; h and B e All are trap coefficients; n ohe and n oht All trap densities are calculated from surface charge decay curves; D h and D e All are trapping coefficients positively correlated with the trap energy level, calculated from the surface charge decay curve; S0, S1, S2, and S3 are all recombination coefficients.

[0037] When charge carriers are injected into the XLPE sample, the current density is calculated using formula (8):

[0038]

[0039] Where, j h (r0,z0,t) and j e (r d ,z d ,t) represent the injection current densities of holes and electrons, respectively; A is Richard's constant; w hi and w ei , respectively, represent the injection barriers for electrons and holes; e is the charge of a single charge.

[0040] When charge carriers are extracted from the XLPE sample, the current density is calculated using formula (9):

[0041]

[0042] Among them, C h and C e These are the extraction coefficients for electrons and holes, respectively;

[0043] Based on formulas (6), (7), (8) and (9), the electric field E(r,z,t) distribution inside XLPE samples of different thicknesses can be obtained.

[0044] The aforementioned method for calculating the breakdown field strength of cable insulation of different thicknesses at different temperatures, specifically when the electron energy is greater than the trap energy level calculated from the surface potential decay experiment, determines the breakdown of the XLPE sample as follows:

[0045] Introducing electric charge energy To determine whether an XLPE sample has broken down, charge energy is required. The calculation formula is shown in equation (10):

[0046]

[0047] Where λ is the mean free path length of the charge;

[0048] When the charge energy exceeds the trap energy level calculated by equation (5), the XLPE sample can be determined to be broken down. At this time, the voltage applied across the XLPE sample is the breakdown voltage of the XLPE sample.

[0049] The aforementioned calculation method for the breakdown field strength of cable insulation of different thicknesses at different temperatures, based on formulas (5) and (10), determines breakdown when the charge energy is greater than the trap energy level, and constructs formula (11) for determining the DC breakdown field strength of XLPE samples:

[0050]

[0051] In the aforementioned method for calculating the breakdown field strength of cable insulation of different thicknesses at different temperatures, step 3, the DC breakdown field strength prediction model of the XLPE sample is shown in formula (12):

[0052]

[0053] Where E(d) is the DC breakdown field strength of an XLPE sample with thickness d; α is the breakdown field strength of an XLPE sample with a thickness of one millimeter; and β is the characteristic of how quickly the breakdown field strength changes with thickness.

[0054] A1, B1, and C1 are all constants related to DC breakdown field strength, while A2, B2, and C2 are constants reflecting the rate of change of DC breakdown field strength with thickness; T is the test temperature.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] 1. This invention provides a method for calculating the breakdown field strength of cable insulation of different thicknesses at different temperatures. For XLPE granules used for cable insulation to be evaluated, it is only necessary to prepare XLPE samples of different thicknesses using a flat plate hot pressing method, test the surface potential decay curves of the XLPE samples at different temperatures, obtain the distribution law of trap energy levels and trap density of the XLPE samples, construct a bipolar carrier model of the XLPE samples, and calculate the DC breakdown field strength of the XLPE samples based on the relationship between charge energy and the magnitude of the trap energy levels of the XLPE samples. A calculation model for the DC breakdown field strength of XLPE samples of different thicknesses at different temperatures is then constructed. Subsequently, the DC breakdown field strength of the XLPE granules to be evaluated can be assessed at any temperature and thickness based on the DC breakdown field strength calculation model. This invention can accurately evaluate the DC breakdown field strength of various XLPE samples, is convenient to operate, has strong universality, and has high accuracy compared with actual experiments. This invention can significantly reduce the repetitive experimental work of researchers, improve research efficiency, and provide cable manufacturers with a scientific analytical means for designing the thickness of high-temperature resistant, high-capacity XLPE cables.

[0057] 2. In this invention, α and β are constants related to the test temperature, and are fitted based on the breakdown field strength of XLPE samples of different thicknesses at different temperatures obtained in step 2; where α represents the DC breakdown field strength of an XLPE sample with a thickness of 1 mm, and α continuously decreases with increasing temperature until it approaches a constant value; β represents the trend of the DC breakdown field strength of the XLPE sample with thickness, and the larger β is, the faster the DC breakdown field strength of the XLPE sample decreases with increasing thickness, and β also continuously decreases with increasing temperature until it approaches a constant value; in this invention, α and β are fitted in the form of a power function, which conforms to the trend of α and β.

[0058] 3. This invention calculates the carrier migration and energy changes inside the XLPE sample. When the carrier energy exceeds the energy level barrier, the XLPE sample can be determined to be broken down. This invention simulates the migration of electrons and holes inside the XLPE sample using a bipolar carrier model and ultimately determines whether the XLPE sample is broken down. It introduces a transport equation to characterize the movement of charge and holes inside the XLPE sample, introduces a Poisson equation to characterize the relationship between carrier density and the magnitude of the electric field inside the XLPE sample, and introduces a continuity equation to characterize the recombination of electrons and holes. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of the process structure of the present invention;

[0060] Figure 2 This is a carrier distribution diagram of the XLPE sample;

[0061] Figure 3 This is the charge energy distribution diagram of the XLPE sample;

[0062] Figure 4 This is a graph showing the measured DC breakdown data of XLPE samples of different thicknesses at 30℃.

[0063] Figure 5 This is a graph showing the measured DC breakdown data of XLPE samples of different thicknesses at 50℃.

[0064] Figure 6 This is a graph showing the measured DC breakdown data of XLPE samples of different thicknesses at 70℃.

[0065] Figure 7 This is a graph showing the measured DC breakdown data of XLPE samples of different thicknesses at 90℃. Detailed Implementation

[0066] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the present invention.

[0067] Example: Calculation method for the breakdown field strength of cable insulation of different thicknesses at different temperatures, structure as follows. Figure 1 As shown, it includes the following steps:

[0068] Step 1: Conduct surface potential decay experiments on XLPE samples of different thicknesses to obtain surface potential decay curves of XLPE samples;

[0069] In step S1, the preparation of the XLPE samples of different thicknesses is as follows: XLPE granules of mass m are weighed, and the XLPE granules are evenly placed in a mold of area S using a flat plate hot pressing method. The mold is then placed in a flat plate vulcanizing machine for high-temperature and high-pressure vulcanization. After complete vulcanization, the mold and the XLPE samples are removed. At least four different thicknesses of XLPE samples are prepared. The mass m of the XLPE granules satisfies the functional relationship shown in formula (1):

[0070] m=ρ·d; (1)

[0071] Where ρ is the density of XLPE granules; d is the thickness of the XLPE sample.

[0072] In this example, a 90×90mm rectangular stainless steel plate with a thickness of 0.1mm and a central cutout was selected as the mold. XLPE granules with a density of 0.97g / cm³ were used. 3 ;

[0073] In this embodiment, the required mass of XLPE granules for XLPE samples of different thicknesses is calculated according to formula (1), as shown in Table 1:

[0074] category XLPE sample thickness / mm XLPE granule mass / g 1 0.1 0.7857 2 0.2 1.5714 3 0.3 2.3571 4 0.4 3.1428

[0075] Table 1. Granule mass corresponding to XLPE samples of different thicknesses

[0076] XLPE granules of different masses were placed into rectangular molds, which were then placed in a flat vulcanizing machine. The molds were pre-pressed at 120°C for 5 minutes, followed by vulcanization at 180°C for 20 minutes under a pressure of 15 MPa. Four XLPE samples of each thickness were prepared.

[0077] After obtaining the XLPE sample, wipe the front and back of the XLPE sample with anhydrous ethanol to ensure that there is no dirt residue on the surface of the XLPE sample, and place the wiped XLPE sample in a ventilated place for 5 minutes to ensure that the anhydrous ethanol evaporates completely; use a thickness gauge with an accuracy of at least 0.01 mm to measure the thickness of the XLPE sample at at least 5 different positions, and calculate the average thickness of each XLPE sample according to formula (2).

[0078]

[0079] Where d XLPE d represents the average thickness of the XLPE pattern. i The thickness of the XLPE sample obtained from the i-th measurement is denoted as ; i represents the number of measurements, i = 1, 2, 3...N; and N represents the total number of measurements performed.

[0080] In this embodiment, the thickness of the cross-linked polyethylene XLPE sample is calculated according to formula (2) as follows:

[0081] As shown in Table 2:

[0082]

[0083]

[0084] Table 2. Granule mass corresponding to XLPE samples of different thicknesses.

[0085] In step 1, a surface potential decay experiment is performed on the XLPE sample. The XLPE sample is heated to the experimental temperature, and the surface of the XLPE sample is charged by corona discharge. The decay of the surface potential of the XLPE sample over time is recorded to obtain the surface potential decay curve of the XLPE sample. The surface potential decay experiment on the XLPE sample meets the following conditions:

[0086] 1) The XLPE sample is placed completely flat on the ground electrode, and the distance between the equalizing grid and the XLPE sample to be tested, and between the equalizing grid and the needle electrode is kept constant; the ambient temperature and humidity remain constant during the test.

[0087] 2) The ground electrode is heated by a thermocouple, and the temperature of the XLPE sample is detected by a temperature sensor. The surface potential decay measurement is started only after the XLPE sample is stable at the test temperature for 5 minutes. The measurement is performed at at least four different temperatures for each thickness of XLPE sample.

[0088] 3) The voltage applied to the needle electrode is -8kV, the voltage applied to the equalizing grid is -4kV, and the charging time is 3min. After charging is completed, the XLPE sample should be moved to the potentiometer within 5s to record the decay of the surface potential. The recording time is 40min.

[0089] Step 2: Obtain the trap parameters of XLPE samples with different thicknesses based on the surface potential decay curves of XLPE samples with different thicknesses. Substitute the trap parameters into the bipolar carrier model to calculate the change of the electronic energy inside the XLPE sample with the pressure time. When the electronic energy is greater than the trap energy level calculated by the surface potential decay experiment, the XLPE sample is determined to be broken down.

[0090] In step 2, the step of obtaining the trap parameters of XLPE samples with different thicknesses based on the surface potential decay curves of XLPE samples with different thicknesses is as follows:

[0091] First, the surface potential decay curve is fitted using a double natural exponential function, and the fitting formula is shown in formula (3):

[0092]

[0093] Where V(t) represents the decay of the surface potential of the XLPE sample over time; t is the test time; A, B, t1, and t2 are all fitting constants, as shown in Table 3 in this embodiment:

[0094] category Temperature / °C A B <![CDATA[t1]]> <![CDATA[t2]]> Sample 1 30 0.375 1.136 217.644 7067.261 Sample 2 50 0.821 0.553 203.132 9211.382 Sample 3 70 1.098 0.056 243.636 15892.378 Sample 4 90 1.260 0.075 77.621 9.946 Sample 5 30 0.381 1.138 250.819 7667.283 Sample 6 50 0.869 0.632 268.569 8901.214 Sample 7 70 1.112 0.066 263.146 23892.197 Sample 8 90 1.300 0.085 105.621 15.945 Sample 9 30 0.379 1.1147 260.188 8067.261 Sample 10 50 0.834 0.623 311.636 9012.678 Sample 11 70 1.122 0.061 313.785 33892.379 Sample 12 90 1.360 0.096 152.621 19.136 Sample 13 30 0.381 1.151 320.845 9118.262 Sample 14 50 0.815 0.661 293.743 10001.235 Sample 15 70 1.243 0.028 403.846 36892.123 Sample 16 90 1.412 0.121 212.621 15.945

[0095] Table 3 shows the values ​​of A, B, t1, and t2.

[0096] Next, the trap energy level distribution of XLPE samples with different thicknesses was obtained based on the test time and test temperature. The calculation process is shown in formula (4):

[0097]

[0098] Among them, E T For the trap energy level; k B is Boltzmann constant; T is the test temperature; h is Planck's constant; v is the vibrational frequency of molecules inside the XLPE sample;

[0099] Then, based on the surface potential decay curve obtained by fitting formula (3) over time, the trap charge density of XLPE samples with different thicknesses is obtained by differentiation as shown in formula (5):

[0100]

[0101] Among them, Q s (t) represents the trap charge density; ε0 represents the vacuum permittivity; ε r V is the relative permittivity; V(t) represents the decay of the surface potential of the XLPE sample over time; q e The amount of charge per unit charge;

[0102] In this embodiment, the trap energy levels and trap densities of XLPE samples of different thicknesses at different temperatures are shown in Table 4:

[0103]

[0104]

[0105] Table 4. Trap energy levels and trap densities of XLPE samples of different thicknesses at different temperatures.

[0106] Based on formulas (4) and (5), the trapping parameters of XLPE samples with different thicknesses can be obtained.

[0107] Substituting the trap parameters into the bipolar carrier model, the change of electronic energy inside the XLPE sample with the pressure time is calculated as follows: Bipolar carrier models of XLPE samples with different thicknesses are introduced to simulate the migration of carriers inside XLPE samples with different thicknesses; the trap energy levels and trap densities of XLPE samples with different thicknesses at different temperatures are substituted into the bipolar carrier model, and the charge transport inside the XLPE sample is simulated according to formula (6) to obtain the charge distribution inside the XLPE sample, where the DC voltage across the XLPE sample gradually increases from 0 kV at a rate of 1 kV / s; the internal migration of carriers can be represented by the transport equation, Poisson equation and continuity equation, as shown in formula (6):

[0108]

[0109] In this context, the subscript 'a' represents different types of charge carriers, specifically free electrons (eμ), trapped electrons (et), free holes (hμ), and trapped holes (ht); j a (r,z,t) represents the magnitude of the current density of carrier a at time t in the r,z coordinate system; μ a n is the mobility of carrier a; a (r,z,t) represents the charge density of carrier a at time t in the r,z coordinate system; D fa ρ(r,z,t) is the decongestion coefficient; E(r,z,t) is the electric field intensity at time t in the r,z coordinate system; ρ(r,z,t) is the volume charge density at time t in the r,z coordinate system; ε is the dielectric constant of the XLPE sample; s a (r,z,t) represents the interaction and reaction process of different charge carriers at time t in the r,z coordinate system, and is called the source phase;

[0110] Based on the trap energy level and trap density of the XLPE sample, the carrier recombination situation inside the XLPE sample is obtained as shown in Equation (7):

[0111]

[0112] Where s a B is the composite coefficient; h and B e All are trap coefficients; n ohe and n oht All trap densities are calculated from surface charge decay curves; D h and D e All are trapping coefficients positively correlated with the trap energy level, calculated from the surface charge decay curve; S0, S1, S2, and S3 are recombination coefficients; according to formulas (6) and (7), the carrier distribution of the XLPE sample is as follows: Figure 2 As shown;

[0113] When charge carriers are injected into the XLPE sample, the current density is calculated using formula (8):

[0114]

[0115] Where, j h (r0,z0,t) and j e (r d ,z d ,t) represent the injection current densities of holes and electrons, respectively; A is Richard's constant; w hi and w ei , respectively, represent the injection barriers for electrons and holes; e is the charge of a single charge.

[0116] When charge carriers are extracted from the XLPE sample, the current density is calculated using formula (9):

[0117]

[0118] Among them, C h and C e These are the extraction coefficients for electrons and holes, respectively;

[0119] Based on formulas (6), (7), (8) and (9), the electric field E(r,z,t) distribution inside XLPE samples of different thicknesses can be obtained.

[0120] When the electronic energy is greater than the trap energy level calculated from the surface potential decay experiment, the XLPE sample is determined to have broken down specifically by introducing charge energy. To determine whether an XLPE sample has broken down, charge energy is required. The calculation formula is shown in equation (10):

[0121]

[0122] Where λ is the mean free path length of the charge; the charge energy distribution inside the XLPE sample is calculated according to formula (10) as follows: Figure 3 As shown;

[0123] When the charge energy exceeds the trap energy level calculated by equation (5), the XLPE sample can be determined to be broken down. At this time, the voltage applied across the XLPE sample is the breakdown voltage of the XLPE sample.

[0124] Based on formulas (5) and (10), breakdown is determined when the charge energy is greater than the trap energy level. Formula (11) for determining the DC breakdown field strength of XLPE samples is then constructed:

[0125]

[0126] When the internal charge energy of the XLPE sample is greater than the trap energy level of the XLPE sample in Table 4, the XLPE sample is determined to be broken down. In this embodiment, the breakdown field strength of the XLPE sample is recorded as shown in Table 5:

[0127]

[0128]

[0129] Table 5. Breakdown field strength of XLPE samples of different thicknesses at different temperatures.

[0130] Step 3: As Figures 4 to 7 As shown, the DC breakdown field strength of XLPE samples of different thicknesses at different temperatures was recorded, and a DC breakdown field strength prediction model for XLPE samples was constructed.

[0131] In step 3, the DC breakdown field strength prediction model for the XLPE sample is shown in formula (12):

[0132]

[0133] Where E(d) is the DC breakdown field strength of an XLPE sample with thickness d; α is the breakdown field strength of an XLPE sample with a thickness of one millimeter; and β is the characteristic of how quickly the breakdown field strength changes with thickness.

[0134] A1, B1, and C1 are all constants related to DC breakdown field strength; A2, B2, and C2 are all constants reflecting the rate of change of DC breakdown field strength with thickness; T is the test temperature.

[0135] α and β are both constants related to the test temperature, and are fitted based on the breakdown field strength of XLPE samples of different thicknesses at different temperatures obtained in step S4; where α represents the DC breakdown field strength of a 1mm thick XLPE sample, and α decreases continuously with increasing temperature until it approaches a constant value; β represents the trend of the DC breakdown field strength of the XLPE sample with thickness, and the larger β is, the faster the DC breakdown field strength of the XLPE sample decreases with increasing thickness, and β also decreases continuously with increasing temperature until it approaches a constant value; in this invention, a power function is used to fit α and β, which conforms to the trend of α and β; in this embodiment, the parameter distribution of the breakdown field strength / thickness fitting model at different temperatures is shown in Table 6:

[0136] Temperature / °C Parameter α Parameter β 30 148.8 0.45 50 136.1 0.28 70 129.8 0.18 90 126.7 0.12

[0137] Table 6. Parameter distribution of the breakdown field strength / thickness fitting model at different temperatures.

[0138] Based on formula (12) and Table 6, the calculation model for the temperature, thickness and DC breakdown field strength of this type of XLPE granules can be obtained as shown in formula (13):

[0139]

[0140] Step 4: Based on the thickness and operating temperature of any XLPE sample to be tested, calculate the DC breakdown field strength of the XLPE sample to be tested using the DC breakdown field strength prediction model.

[0141] To further demonstrate the effectiveness of this invention, a DC breakdown test was conducted using the same XLPE sample. A ball-plate electrode was used in the experiment; the ball's diameter was 20 mm, and the metal plate's diameter was 25 mm, with the plates coaxial. To avoid surface flashover, the ball electrode was immersed in No. 25 transformer oil. A heating rod and thermoelectric electrodes were used to heat the transformer oil at a voltage ramp rate of 1 kV / s. The test results are as follows: Figure 3 As shown; from Figure 3 It can be seen that the DC breakdown field strength of XLPE samples of different thicknesses at different temperatures is basically consistent with the simulation results. The simulation results are lower than the experimental results at 50℃. This is because the XLPE sample trap parameters used in this invention are more sensitive to temperature. Therefore, the DC breakdown field strength prediction model of this invention is more accurate at high temperatures. This result further proves the effectiveness of the invention.

[0142] In summary, this invention provides a method for calculating the breakdown field strength of cable insulation of different thicknesses at different temperatures. For the XLPE granules used for cable insulation to be evaluated, it is only necessary to prepare XLPE samples of different thicknesses using a flat plate hot pressing method, test the surface potential decay curves of the XLPE samples at different temperatures, obtain the distribution law of trap energy levels and trap density of the XLPE samples, construct a bipolar carrier model of the XLPE samples, and calculate the DC breakdown field strength of the XLPE samples based on the relationship between charge energy and the magnitude of the trap energy levels of the XLPE samples. A calculation model for the DC breakdown field strength of XLPE samples of different thicknesses at different temperatures is then constructed. Subsequently, the DC breakdown field strength of the XLPE granules to be evaluated can be assessed based on this model under any temperature and any thickness. This invention can accurately evaluate the DC breakdown field strength of various XLPE samples, has the advantages of convenient operation and strong universality, and shows high accuracy compared with actual experiments. This invention can significantly reduce the repetitive experimental work of researchers, improve research efficiency, and provide cable manufacturers with a scientific analytical means for designing the thickness of high-temperature resistant, high-capacity XLPE cables.

Claims

1. A method for calculating the breakdown field strength of different thicknesses of cable insulation at different temperatures, characterized by: Comprising the following steps: Step 1: surface potential decay experiment is carried out on XLPE samples of different thicknesses, and the surface potential decay curve of the XLPE sample is obtained; Step 2: the trap parameters of the XLPE sample of different thicknesses are obtained according to the surface potential decay curve of the XLPE sample of different thicknesses, the trap parameters are substituted into the bipolar carrier model, the change of the electron energy in the XLPE sample with the pressure time is calculated, and when the electron energy is greater than the trap energy level calculated by the surface potential decay experiment, the XLPE sample is determined to be breakdown; Step 3: the DC breakdown field strength of the XLPE sample at different temperatures is recorded, and a DC breakdown field strength prediction model of the XLPE sample is constructed; the DC breakdown field strength prediction model of the XLPE sample is shown as formula (12): ； （12） wherein, is the DC breakdown field strength of an XLPE sample having a thickness of is the breakdown field strength of an XLPE sample having a thickness of one millimeter; is a constant representing how quickly the breakdown field strength changes with thickness; , and are constants related to the DC breakdown field strength, , and are constants related to how quickly the DC breakdown field strength changes with thickness; is the test temperature;​ Step 4: according to the thickness and operating temperature of any XLPE sample to be measured, the DC breakdown field strength of the XLPE sample to be measured is calculated by using the DC breakdown field strength prediction model.

2. The method of claim 1, wherein: In step 1, the preparation of the XLPE sample with different thicknesses is as follows: XLPE granules with a mass of are uniformly placed in a mold with an area of , the mold is placed in a flat vulcanizing machine for high-temperature and high-pressure vulcanization, and after waiting for complete vulcanization, the mold and the XLPE sample are taken out; wherein the mass of the XLPE granules satisfies the functional relationship as shown in formula (1): ；（1） wherein, is the density of the XLPE pellets; is the thickness of the XLPE sample.

3. The method of claim 2, wherein: After the XLPE sample is prepared, a thickness gauge with an accuracy of at least 0.01 mm is used to measure the thickness of the XLPE sample at at least 5 different positions, and the average thickness of each XLPE sample is calculated according to formula (2): ；（2） wherein is the average thickness of the XLPE sample; is the thickness of the XLPE sample obtained from the measurement; is the number of measurements, ; N is the total number of measurements performed.

4. The method of claim 1, wherein: In step 1, the surface potential decay experiment on the XLPE sample satisfies the following conditions: 1) The XLPE sample is completely placed on the ground electrode, and the distances between the voltage grading net and the XLPE sample to be measured, and between the voltage grading net and the needle electrode are kept consistent; the ambient temperature and humidity remain unchanged during the test; 2) The ground electrode is heated by a thermocouple, and the temperature of the XLPE sample is detected by a temperature sensor, so that the XLPE sample is stabilized at the test temperature for 5-7 min before the surface potential decay measurement is started, and the XLPE sample of each thickness is measured at at least multiple different temperatures; 3) The voltage applied to the needle electrode is-8 kV, the voltage applied to the voltage grading net is-4 kV, and the charging time is 3-5 min; after the charging is completed, the XLPE sample should be moved to the potentiometer within 3-5 s to record the surface potential decay, and the recording time is 35-45 min.

5. The method of claim 1, wherein: In step 2, the trap parameters of the XLPE sample of different thicknesses are obtained according to the surface potential decay curve of the XLPE sample of different thicknesses as follows: First, the surface potential decay curve is fitted by a double natural exponential function, and the fitting formula is shown as formula (3): ；（3） wherein, is the decay of the surface potential of the XLPE sample over time; , , and are fitting constants; is the test time; Then, the trap energy level distribution of the XLPE sample of different thicknesses is obtained according to the test time and test temperature, and the calculation process is shown as formula (4): ；（4） wherein, is a trap energy level; is the Boltzmann constant; is the test temperature; is the Planck constant; is the vibration frequency of the molecules within the XLPE sample; Then, the trap charge density of the XLPE sample of different thicknesses is obtained by differentiating the surface potential decay curve fitted by formula (3) as shown in formula (5): ；（5） wherein, is the trapped charge density; is the vacuum permittivity; is the relative permittivity; is the decay of the surface potential of the XLPE sample with time; is the charge quantity per unit charge; is the thickness of the XLPE sample; Based on formula (4) and formula (5), the trap parameters of the XLPE sample of different thicknesses are obtained.

6. The method of claim 5, wherein: The change of the electron energy in the XLPE sample with the pressure time is calculated by substituting the trap parameters into the bipolar carrier model as follows: The bipolar carrier model was introduced to simulate the migration of the carriers in XLPE samples with different thicknesses, as shown in equation (6): ；（6） where subscript represents different types of carriers, which can be specifically divided into free electrons , trapped electrons , free holes and trapped holes ; is the current density of the carrier at time in the coordinate system ; is the mobility of the carrier ; is the charge density of the carrier at time in the coordinate system ; is the detrapping coefficient; is the electric field intensity at time in the coordinate system ; is the bulk charge density at time in the coordinate system ; is the dielectric constant of the XLPE sample; is the process of interaction between different carriers at time in the coordinate system , which is called source phase, and the calculation method is shown in equation (7):​​​​​ ；（7） wherein and are both trap coefficients; and are both trap densities calculated from surface charge decay curves; and are both trap energy level positive correlation detrapping coefficients calculated from surface charge decay curves; , , and are all recombination coefficients; When the carriers were injected into the XLPE sample, the current density was calculated by equation (8): ；（8） wherein and respectively the injection current density of holes and electrons; is the Richard constant; and respectively the injection barrier of electrons and holes; is the charge quantity of a single charge; When the carriers were extracted from the XLPE sample, the current density was calculated by equation (9): ；（9） wherein, and are the extraction coefficients for electrons and holes, respectively; Based on formula (6), formula (7), formula (8) and formula (9), the electric field distribution in the XLPE sample with different thicknesses is obtained distribution.

7. The method of claim 6, wherein: When the electron energy was greater than the trap energy level calculated by the surface potential decay experiment, the XLPE sample was determined to be breakdown, and the specific breakdown voltage was: Charge energy introduced Determination of whether XLPE sample is breakdown, charge energy The calculation formula is shown in equation (10): ； （10） wherein is the mean free path length of the charge carriers; When the charge energy was greater than the trap energy level calculated by equation (4), the XLPE sample was determined to be breakdown, and the voltage applied across the XLPE sample was the breakdown voltage of the XLPE sample.

8. The method of claim 7, wherein: According to equations (4) and (10), when the charge energy is greater than the trap energy level, the breakdown is determined, and the determination formula (11) of the DC breakdown field strength of the XLPE sample is constructed: ，（11）。

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