Method for calculating space charge distribution of cable factory joint at different temperatures

Abstract

The invention discloses a method for calculating space charge distribution of a cable factory joint at different temperatures, which comprises the following steps of: 1, cutting a sample of the cable factory joint to obtain an insulation sample, and measuring the average thickness; 2, measuring conductance current at different temperatures, calculating the carrier mobility, and fitting the temperature and the carrier mobility of the insulation sample; 3, testing a positive-voltage and negative-voltage charging isothermal surface potential attenuation curve to obtain electron trap energy levels, electron trap densities, hole trap energy levels and hole trap densities at different temperatures; 4, setting boundary conditions, and establishing a bipolar carrier model; and 5, substituting the carrier mobility, the electron trap energy level, the electron trap density, the hole trap energy level and the hole trap density into the bipolar carrier model to obtain space charge distribution. According to the method, the space charge distribution in the cable factory joint can be quickly and accurately calculated, and the fault risk caused by unreasonable space charge distribution is reduced.

Description

Technical Field

[0001] The present invention belongs to the field of high voltage and insulation technology, and specifically relates to a method for calculating the spatial charge distribution of a cable factory joint at different temperatures. Background Art

[0002] At present, the proportion of renewable energy power generation in the power system is increasing, among which offshore wind power has been vigorously developed due to its rich resources and high power generation hours. Large-capacity ultra-high voltage DC submarine cables with cross-linked polyethylene (XLPE) as insulation material are widely used in DC transmission fields such as offshore wind power, offshore photovoltaics and long-distance cross-sea power transmission due to their simple preparation process and large transmission capacity.

[0003] During the production process of factory joints, it is necessary to inject newly melted XLPE into the main insulation of the submarine cable that has been polished into a cone, and then form the restored insulation after high-temperature and high-pressure vulcanization. Since the main insulation is subjected to two high-temperature and high-pressure vulcanizations, and the restored insulation is only subjected to one, there will be an interface between the main insulation and the restored insulation. The difference in carrier transport velocity and trap distribution on both sides of the interface can easily cause the accumulation of space charge at and around the interface, accelerate material aging, and ultimately cause insulation failure. The calculation method of the spatial charge distribution of cable insulation performance at different temperatures in the prior art is not accurate enough and the calculation speed is slow, and there is a lack of comprehensive consideration and accurate quantitative calculation method for the complex carrier behavior inside the cable joint, including the relationship between carrier mobility, electron trap energy level, electron trap density, hole trap energy level and hole trap density and the spatial charge distribution. Summary of the invention

[0004] The purpose of the present invention is to provide a method for calculating the spatial charge distribution of a cable factory joint at different temperatures. The present invention can quickly and accurately calculate the spatial charge distribution inside the cable factory joint, reducing the risk of failure caused by unreasonable spatial charge distribution.

[0005] The technical solution of the present invention is a method for calculating the spatial charge distribution of a cable factory joint at different temperatures, comprising the following steps:

[0006] Step 1: Cut the factory joint sample of the cable to be tested by the ring cutting method to obtain the insulation sample, and measure the average thickness of the insulation sample;

[0007] Step 2: The conductance current of the insulating sample is measured at different temperatures using a three-electrode method. Based on the average thickness and conductance current, the carrier mobility of the different insulating samples is calculated, and the relationship between temperature and the carrier mobility of the insulating sample is fitted.

[0008] Step 3: Test the isothermal surface potential decay curve of the insulating sample after positive pressure charging and negative pressure charging, and use the isothermal surface potential decay curve to obtain the electron trap energy level, electron trap density, hole trap energy level and hole trap density of the insulating sample at different temperatures;

[0009] Step 4: Set boundary conditions and establish a bipolar carrier model for cable factory joints based on the carrier mobility, electron trap energy level, electron trap density, hole trap energy level and hole trap density of different insulating samples;

[0010] Step 5: Substitute the carrier mobility, electron trap energy level, electron trap density, hole trap energy level and hole trap density of the cable factory joint insulation sample into the cable factory joint bipolar carrier model, and calculate the spatial charge distribution inside the cable factory joint by the cable factory joint bipolar carrier model.

[0011] 3. In the aforementioned method for calculating the spatial charge distribution of the cable factory joint at different temperatures, in step 1, the ring cutting sampling positions are the main insulation, the recovery insulation and the interface between the main insulation and the recovery insulation; the thickness of the insulation sample is 0.2 mm; the process of measuring the average thickness includes measuring the thickness of the insulation sample at least five different positions, and calculating the thickness of the insulation sample, and the calculation formula is as follows:

[0012]

[0013] Among them, d insul is the thickness of the insulating sample, d i is the thickness of the insulating sample obtained by the i-th measurement, and N is the number of measurements.

[0014] In the aforementioned method for calculating the spatial charge distribution of the cable factory joint at different temperatures, in step 2, the process of measuring the conductance current at different temperatures by the three-electrode method includes placing the insulating sample on the three-electrode structure, setting the test field strength to 40-60MV / m, and controlling the test temperature to 20°C, 30°C, 40°C, 50°C, 60°C, 70°C, and 80°C; waiting for the internal charge of the insulating sample to completely dissipate and the temperature to stabilize, performing a polarization operation for 20-40 minutes and a depolarization operation for 5-15 minutes on the insulating sample, and taking the average of the last 20-40 data points in the polarization process as the measured value of the conductance current.

[0015] In the aforementioned method for calculating the spatial charge distribution of the cable factory joint at different temperatures, the field strength is 50MV / m, the test temperature is controlled to 30°C, 50°C, and 70°C; the polarization operation time is 30 minutes, the depolarization operation time is 10 minutes, and the average value of the last 30 data points in the polarization process is taken as the measured value of the conductance current.

[0016] In the aforementioned method for calculating the spatial charge distribution of the cable factory joint at different temperatures, in step 2, based on the average thickness and the conductance current, the conductance current is divided by the contact area between the conductivity test electrode and the insulating sample to obtain the conductance current density. The calculation formula for the carrier mobility of the different insulating samples is as follows:

[0017]

[0018] Where μ is the carrier mobility of the insulating sample, J is the current density measured by the three-electrode method, ε0 is the vacuum dielectric constant, and ε r is the relative dielectric constant, V is the voltage amplitude applied to the insulating sample;

[0019] The carrier mobility of different insulating samples at different temperatures is fitted, and the fitting formula for the relationship between temperature and the carrier mobility of the insulating sample is as follows:

[0020]

[0021] Where μ0 and E a are constants obtained in the function fitting process, k B is the Boltzmann constant, and T is the test temperature of the three-electrode method.

[0022] In the aforementioned method for calculating the spatial charge distribution of the cable factory joint at different temperatures, in step three, the process of testing the isothermal surface potential decay curve of the insulating sample after positive pressure charging and negative pressure charging includes placing the insulating sample flat on the ground electrode, keeping the distance between the voltage equalizing network and the insulating sample, and the distance between the voltage equalizing network and the needle electrode consistent, and controlling the test temperature to 20°C, 30°C, 40°C, 50°C, 60°C, 70°C, and 80°C; charging the insulating sample at negative pressure, the voltage applied to the needle electrode is -10 to -5kV, the voltage applied to the voltage equalizing network is -6 to -2kV, and the charging time is 2 to 4min; when charging the insulating sample at positive pressure, the voltage applied to the needle electrode is 5 to 10kV, the voltage applied to the voltage equalizing network is 2 to 4kV, and the charging time is 2 to 4min; recording the isothermal surface potential decay curve of the insulating sample within 5s after the charging is completed, and the recording time is 30 to 50min.

[0023] In the aforementioned method for calculating the spatial charge distribution of the cable factory joint at different temperatures, the hole trap energy level and the electron trap energy level are calculated according to the test time and test temperature of the isothermal surface potential decay curve under positive pressure charging and negative pressure charging, respectively, and the calculation formula is as follows:

[0024]

[0025] In the formula, E Tis the trap energy level, h is the Planck constant, T SPD is the test temperature of the isothermal surface potential decay curve, v is the vibration frequency of the molecules inside the insulating sample, and t is the time;

[0026] The hole trap density and the electron trap density are calculated by differentiating the isothermal surface potential decay curves under positive pressure charging and negative pressure charging, respectively, and the calculation formula is as follows:

[0027]

[0028] In the formula, Q s (t) is the trap density, V(t) is the isothermal surface potential decay curve of the insulating sample over time, q e is the charge of the electron.

[0029] In the aforementioned method for calculating the spatial charge distribution of the cable factory joint at different temperatures, in step 4, the process of setting the boundary conditions includes:

[0030] Set the boundary conditions of the bulk insulation close to the conductor side and calculate the current density of hole injection and electron extraction. The formula is as follows:

[0031]

[0032] In the formula, j h (r0, z0, t) and j e (r0, z0, t) are the current densities of hole injection and electron extraction on the conductor side of the bulk insulation, respectively. T(r0, z0, t) is the temperature of the bulk insulation of the cable factory connector on the conductor side. E(r0, z0, t) represents the electric field strength at time t in the r, z coordinate system. A is the Richard constant, k is the Boltzmann constant, and w hi and w ei The injection barrier for electrons and holes, e is the charge of a single charge, C e is the electron extraction coefficient, n eμ (r0, z0, t) is the charge density of the free electron eμ, μ e is the electron carrier mobility obtained by the three-electrode method, ε is the dielectric constant of the insulating sample;

[0033] Set the boundary conditions at the interface between the bulk insulation and the restoration insulation, and the current density at the interface between the bulk insulation and the restoration insulation. The formula is as follows:

[0034]

[0035] Among them, j h (r, z, t) is the current density of holes at the interface between bulk insulation and recovery insulation, μh is the hole carrier mobility, C ih is the barrier coefficient of the interface between the bulk insulation and the recovery insulation for holes, n hμ (r, z, t) is the charge density of the free hole hμ, j e (r, z, t) is the current density of electrons at the interface between bulk insulation and recovery insulation, μe is the electron carrier mobility, C ie is the barrier coefficient of the interface between bulk insulation and recovery insulation for electrons, n eμ (r, z, t) is the charge density of free electrons eμ;

[0036] Set the boundary conditions of the recovery insulation close to the outer shield side and calculate the current density of hole extraction and electron injection. The formula is as follows:

[0037]

[0038] Among them, j e (r d , Z d , t) and j h (r d , z d , t) are the current densities of electron injection and hole extraction near the outer shielding side of the recovery insulation, T(r d , z d , t) is the temperature of the cable factory joint where the insulation is restored near the outer shield side, E(r d , z d , t) represents the electric field intensity at time t in the r, z coordinate system, C h is the extraction coefficient of the hole, n hμ (r d ,Z d ,t) is the charge density of free holes hμ, μ h is the hole carrier mobility obtained by the three-electrode method.

[0039] In the aforementioned method for calculating the spatial charge distribution of the cable factory joint at different temperatures, in step 4, based on the carrier mobility, electron trap energy level, electron trap density, hole trap energy level and hole trap density of different insulating samples, the formula of the bipolar carrier model of the cable factory joint is as follows:

[0040]

[0041] The subscript a represents different types of carriers, which can be divided into free electrons eμ, trapped electrons et, free holes hμ, trapped holes h t ;j a(r, z, t) represents the current density of carrier a at time t in the r, z coordinate system; μ a is the carrier mobility of carrier a; n a (r, z, t) represents the charge density of carrier a at time t in the r, z coordinate system; D fa represents the escape coefficient; E(r, z, t) represents the electric field intensity at time t in the r, z coordinate system, ρ(r, z, t) represents the volume charge density at time t in the r, Z coordinate system; s a (r, z, t) represents the process of interaction between different carriers at time t in the r, z coordinate system, which is called the source phase.

[0042] In the aforementioned calculation method of the spatial charge distribution at different temperatures of the cable factory joint, in step 5, the electron and hole trap parameters at different insulation positions are substituted into the source phase to calculate the spatial charge distribution inside the cable factory joint. The calculation method is shown in the formula:

[0043]

[0044] Among them, S0, S1, S2 and S3 are composite coefficients, B h and B e is the trap coefficient, n oet and n oht are the electron trap density and hole trap density calculated from the surface charge decay curve, D h and D e are the trapping coefficients of holes and electrons, which are positively correlated with the trap energy levels calculated from the surface charge decay curve, and s ht , S hμ 、s et and eμ It is the source phase of free electrons eμ, trapped electrons et, free holes hμ, and trapped holes ht.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] The present invention cuts out insulation samples of different insulation positions through the cable factory ring, tests the current density of the insulation samples at different temperatures and the isothermal surface potential decay curves under positive and negative charge charging, obtains the carrier mobility, electron trap energy level, electron trap density, hole trap energy level and hole trap density of different insulation positions, and constructs the bipolar carrier model of the cable factory joint by setting boundary conditions, and then quickly and accurately calculates the spatial charge distribution inside the cable factory joint according to the model, which can more accurately evaluate the performance of the cable factory joint under different working temperature environments, help optimize the design and manufacturing process of the cable factory joint in the production process, improve product quality, and reduce the risk of failure caused by unreasonable spatial charge distribution. In addition, the present invention can intuitively analyze the accumulation of spatial charge inside the cable factory joint under actual working conditions for scientific researchers, discover the weak position inside the cable factory joint in advance, and provide scientific analysis means for cable manufacturers to design and develop ultra-high voltage submarine cable factory joints. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart for calculating the spatial charge distribution of the cable factory joint at different temperatures of the present invention;

[0048] Figure 2 This is a schematic diagram of the cable factory joint ring cutting of the present invention;

[0049] Figure 3 It is a geometrical schematic diagram of the cable factory joint simulation model of the present invention;

[0050] Figure 4 It is the spatial charge distribution of the cable factory joint at different temperatures of the present invention. DETAILED DESCRIPTION

[0051] The present invention is further described below in conjunction with the accompanying drawings and embodiments, but they are not intended to limit the present invention.

[0052] Embodiment: A method for calculating the spatial charge distribution at different temperatures of a cable factory joint is as follows: Figure 1 As shown, the following steps are included:

[0053] Step 1: Cut the factory joint sample of the cable to be tested by the ring cutting method to obtain the insulation sample, and measure the average thickness of the insulation sample;

[0054] In step one, if Figure 2The figure shows the schematic diagram of the cable factory joint ring cutting. Place the cable factory joint sample on the lathe, press the tool against the outside of the cable factory joint sample, and rotate the cable factory joint sample to start ring cutting. Control the distance between the tool and the cable factory joint sample so that the thickness of the cut sample is about 0.2mm. The factory joint insulation is divided into three parts: main insulation, recovery insulation, and the interface between main insulation and recovery insulation. According to the position of the sample cut during ring cutting, the insulation samples of main insulation, recovery insulation, and the interface between main insulation and recovery insulation are prepared.

[0055] In this embodiment, the insulation sample after cutting and ring cutting is a thin sheet of 5 cm×5 cm in size. The insulation sample is cleaned for 2 minutes using an ultrasonic cleaning machine, and the front and back sides of the cleaned insulation sample are wiped to ensure that no dirt remains. A thickness gauge with an accuracy of at least 0.001 mm is used to measure the thickness of at least 5 different positions of the insulation sample, and the thickness of the insulation sample is calculated using the following calculation formula:

[0056]

[0057] Among them, d insul is the thickness of the insulating sample, d i is the thickness of the insulating sample obtained by the ith measurement, and N is the number of measurements; the calculated average thickness of different insulating samples is shown in Table 1.

[0058] Table 1 Average thickness of different insulation samples

[0059]

[0060] Step 2: The conductance current of the insulating sample is measured at different temperatures using a three-electrode method. Based on the average thickness and conductance current, the carrier mobility of the different insulating samples is calculated, and the relationship between temperature and the carrier mobility of the insulating sample is fitted.

[0061] In this embodiment, an insulating sample is placed on a three-electrode structure. The measuring electrode and the high-voltage electrode in the three-electrode structure are stainless steel cylinders with diameters of 3 cm and 4.5 cm respectively, and the outer side of the measuring electrode is a ring electrode with inner and outer diameters of 3.2 cm and 4.5 cm respectively. The three-electrode structure is placed in a constant temperature drying oven, the test field strength is 50MV / m, and the test temperature is controlled at 30, 50, and 70°C by the oven. During the test, the sample is placed in the equipment for 1 hour or more to completely dissipate the internal charge and stabilize the temperature. The sample is polarized for 30 minutes and depolarized for 10 minutes. The average value of the last 30 data points in the polarization process is taken as the measured value of the conductance current.

[0062] Based on the average thickness and the conductance current, the conductance current is divided by the contact area between the conductivity test electrode and the insulating sample to obtain the conductance current density. The calculation formula for the carrier mobility of the different insulating samples is as follows:

[0063]

[0064] Where μ is the carrier mobility of the insulating sample, J is the current density measured by the three-electrode method, ε0 is the vacuum dielectric constant, and ε r is the relative dielectric constant, V is the voltage amplitude applied to the insulating sample; the carrier mobility of different insulating samples at different temperatures is shown in Table 2.

[0065] The carrier mobility of different insulating samples at different temperatures is fitted, and the fitting formula for the relationship between temperature and the carrier mobility of the insulating sample is as follows:

[0066]

[0067] Where μ0 and E a are constants obtained in the function fitting process, k B is the Boltzmann constant, and T is the test temperature of the three-electrode method.

[0068] Table 2 Carrier mobility of different insulating samples at different temperatures

[0069]

[0070] Step 3: Step 3: Test the isothermal surface potential decay curve of the insulating sample after positive pressure charging and negative pressure charging, and use the isothermal surface potential decay curve to obtain the electron trap energy level, electron trap density, hole trap energy level and hole trap density of the insulating sample at different temperatures;

[0071] In this embodiment, the insulating sample should be placed completely flat on the ground electrode, and the distance between the voltage balancing network and the sample to be tested, and between the voltage balancing network and the needle electrode should be kept consistent. During the isothermal surface potential decay curve test, the ambient temperature and ambient humidity should remain unchanged, and the ambient humidity should be kept below 30%.

[0072] The ground electrode is heated by a thermocouple, and the temperature of the insulating sample is detected by a temperature sensor. The measurement should be started after the insulating sample is stable at the test temperature for 10 minutes. The test temperature is consistent with the temperature range of the three-electrode method for measuring the conduction current, which is 30, 50, and 70°C.

[0073] When conducting negative pressure charging experiments, the voltage applied to the needle electrode is -8kV, the voltage applied to the voltage equalizing network is -4kV, and the charging time is 3min. When conducting positive pressure charging experiments, the voltage applied to the needle electrode is 8kV, the voltage applied to the voltage equalizing network is 4kV, and the charging time is 3min. After charging, the sample should be moved under the potentiometer within 5s to record the decay of the surface potential, and the recording time is 40min.

[0074] The hole trap energy level and electron trap energy level are calculated according to the test time and test temperature of the isothermal surface potential decay curve under positive pressure charging and negative pressure charging, respectively. The calculation formula is as follows:

[0075]

[0076] In the formula, E T is the trap energy level, h is the Planck constant, T SPD is the test temperature of the isothermal surface potential decay curve, v is the vibration frequency of the molecules inside the insulating sample, and t is the time;

[0077] The hole trap density and electron trap density are calculated by differentiating the isothermal surface potential decay curves under positive pressure charging and negative pressure charging, respectively. The calculation formula is as follows:

[0078]

[0079] In the formula, Q s (t) is the trap density, V(t) is the isothermal surface potential decay curve of the insulating sample over time, q e is the charge of the electron;

[0080] The calculated electron trap energy levels, electron trap densities, hole trap energy levels and hole trap densities of different insulating samples at different temperatures are shown in Tables 3 and 4, respectively.

[0081] Table 3 Electron trap energy levels and electron trap densities of different insulating samples at different temperatures

[0082]

[0083] Table 4 Hole trap energy levels and hole trap densities at different temperatures for different insulating samples

[0084]

[0085]

[0086] Step 4: Set boundary conditions and establish a bipolar carrier model for cable factory joints based on the carrier mobility, electron trap energy level, electron trap density, hole trap energy level and hole trap density of different insulating samples;

[0087] In this embodiment, the cable factory joint simulation model is as follows: Figure 3 As shown in Figure 2, the process of setting boundary conditions includes:

[0088] Set the boundary conditions of the bulk insulation close to the conductor side and calculate the current density of hole injection and electron extraction. The formula is as follows:

[0089]

[0090] In the formula, j h (r0, z0, t) and j e (r0, z0, t) are the current densities of hole injection and electron extraction on the conductor side of the bulk insulation, respectively. T(r0, z0, t) is the temperature of the bulk insulation of the cable factory connector on the conductor side. E(r0, z0, t) represents the electric field strength at time t in the r, z coordinate system. A is the Richard constant, k is the Boltzmann constant, and w hi and w ei The injection barrier for electrons and holes, e is the charge of a single charge, C e is the electron extraction coefficient, n eμ (r0, z0, t) is the charge density of the free electron eμ, μ e is the electron carrier mobility obtained by the three-electrode method, ε is the dielectric constant of the insulating sample;

[0091] Set the boundary conditions at the interface between the bulk insulation and the restoration insulation, and the current density at the interface between the bulk insulation and the restoration insulation. The formula is as follows:

[0092]

[0093] Among them, j h (r, z, t) is the current density of holes at the interface between bulk insulation and recovery insulation, μ h is the hole carrier mobility, C ih is the barrier coefficient of the interface between the bulk insulation and the recovery insulation for holes, n hμ (r, z, t) is the charge density of the free hole hμ, j e (r, z, t) is the current density of electrons at the interface between bulk insulation and recovery insulation, μ e is the electron carrier mobility, C ie is the barrier coefficient of the interface between bulk insulation and recovery insulation for electrons, n eμ (r, z, t) is the charge density of free electrons eμ;

[0094] Set the boundary conditions of the recovery insulation close to the outer shield side and calculate the current density of hole extraction and electron injection. The formula is as follows:

[0095]

[0096] Among them, j e (r d ,Z d ,t) and j h (r d , Z d , t) are the current densities of electron injection and hole extraction near the outer shielding side of the recovery insulation, T(r d , z d , t) is the temperature of the cable factory joint where the insulation is restored near the outer shield side, E(r d , z d , t) represents the electric field intensity at time t in the r, z coordinate system, C h is the extraction coefficient of the hole, n hμ (r d ,Z d ,t) is the charge density of free holes hμ, μ h is the hole carrier mobility obtained by the three-electrode method.

[0097] Step 5: Substitute the carrier mobility, electron trap energy level, electron trap density, hole trap energy level and hole trap density of the cable factory joint insulation sample into the cable factory joint bipolar carrier model, and calculate the spatial charge distribution inside the cable factory joint by the cable factory joint bipolar carrier model.

[0098] Based on the set boundary conditions, the carrier mobility calculated in step 2, and the electron trap energy level, electron trap density, hole trap energy level and hole trap density calculated in step 3, the carrier migration in the bulk insulation, the interface between the bulk insulation and the recovery insulation, and the recovery insulation is calculated through the transport equation, Poisson's equation and continuity equation. The formula of the bipolar carrier model of the cable factory joint is as follows:

[0099]

[0100] The subscript a represents different types of carriers, which can be divided into free electrons eμ, trapped electrons et, free holes hμ, trapped holes h t ;j a (r,z ,t ) represents the current density of carrier a at time t in the r, z coordinate system; μ a is the carrier mobility of carrier a; n a(r, z, t) represents the charge density of carrier a at time t in the r, z coordinate system; D fa represents the escape coefficient; E(r, z, t) represents the electric field intensity at time t in the r, z coordinate system, ρ(r, z, t) represents the volume charge density at time t in the r, z coordinate system; s a (r, z, t) represents the process of interaction between different carriers at time t in the r, z coordinate system, which is called the source phase.

[0101] Substituting the electron trap energy level, electron trap density, hole trap energy level and hole trap density at different insulation positions into the source phase, the spatial charge distribution inside the cable factory joint is calculated. The calculation method is shown in the formula:

[0102]

[0103] Among them, S0, S1, S2 and S3 are composite coefficients, B h and B e is the trap coefficient, n oet and n oht are the electron trap density and hole trap density calculated from the surface charge decay curve, D h and D e are the trapping coefficients of holes and electrons, which are positively correlated with the trap energy levels calculated from the surface charge decay curve, and s ht , S hμ 、s et and eμ It is the source phase of free electrons eμ, trapped electrons et, free holes hμ, and trapped holes ht.

[0104] Based on the carrier mobility, electron trap energy level, electron trap density, hole trap energy level and hole trap density of the insulating samples at different insulation positions at 30℃, 50℃ and 70℃, the internal space charge distribution of the cable factory joint under different conditions is calculated. Figure 4 The maximum space charge density and maximum electric field distortion at different temperatures inside the cable factory joint are shown in Table 5.

[0105] Table 5 Maximum charge accumulation and maximum electric field distortion at different temperatures inside the cable factory connector

[0106] temperature 30℃ 50℃ 70℃ <![CDATA[Maximum charge accumulation (C / m 3 )]]> 0.013 0.210 3.637 Maximum electric field distortion (MV / m) 16.673 16.754 17.452

[0107] According to the distribution law of the space charge inside the cable factory joint, it can be found that the charge accumulation near the conductor side at the root of the stress cone of the cable factory joint is the most serious. At the same time, with the increase of temperature, the space charge accumulation becomes more and more serious, and the root of the stress cone is very likely to become a breakdown inducing point. The present invention provides a method for calculating the space charge distribution of the cable factory joint at different temperatures. For the cable factory joint, it is only necessary to cut out the insulation samples of different insulation positions by lathe ring cutting, test the conductivity cable density of the insulation sample at different temperatures and the isothermal surface potential decay curve under positive and negative charge charging, obtain the carrier mobility, electron trap energy level, electron trap density, hole trap energy level and hole trap density of different insulation positions, set the boundary conditions of the bulk insulation, recovery insulation and the interface at their junction, and construct the bipolar carrier model of the cable factory joint. Subsequently, the distribution change of the space charge inside the factory joint with the pressurization time can be evaluated according to the model, and the performance of the cable factory joint under different working temperature environments can be more accurately evaluated, which is helpful to optimize the design and manufacturing process of the cable factory joint in the production process, improve product quality, and reduce the risk of failure caused by unreasonable space charge distribution. In particular, the present invention can calculate and analyze the spatial charge distribution inside the cable factory joint. It is easy to operate and has strong universality. It can enable scientific researchers to intuitively analyze the accumulation of spatial charge inside the cable factory joint under actual working conditions, discover weak locations inside the cable factory joint in advance, and provide scientific analysis means for cable manufacturers to design and develop ultra-high voltage submarine cable factory joints.

[0108] In summary, the present invention can quickly and accurately calculate the spatial charge distribution inside the cable factory joint, reducing the risk of failure caused by unreasonable spatial charge distribution.

Claims

1. A method for calculating the spatial charge distribution of cable factory joints at different temperatures, characterized in that: The following steps are involved: Step 1: Cut the factory joint sample of the cable to be tested by the ring cutting method to obtain the insulation sample, and measure the average thickness of the insulation sample; Step 2: The conductance current of the insulating sample is measured at different temperatures using a three-electrode method. Based on the average thickness and conductance current, the carrier mobility of the different insulating samples is calculated, and the relationship between temperature and the carrier mobility of the insulating sample is fitted. Step 3: Test the isothermal surface potential decay curve of the insulating sample after positive pressure charging and negative pressure charging, and use the isothermal surface potential decay curve to obtain the electron trap energy level, electron trap density, hole trap energy level and hole trap density of the insulating sample at different temperatures; Step 4: Set boundary conditions and establish a bipolar carrier model for cable factory joints based on the carrier mobility, electron trap energy level, electron trap density, hole trap energy level and hole trap density of different insulating samples; Step 5: Substitute the carrier mobility, electron trap energy level, electron trap density, hole trap energy level and hole trap density of the cable factory joint insulation sample into the cable factory joint bipolar carrier model, and calculate the spatial charge distribution inside the cable factory joint by the cable factory joint bipolar carrier model.

2. The method for calculating the spatial charge distribution of the cable factory joint at different temperatures according to claim 1 is characterized by: In step 1, the ring cutting sampling positions are the main insulation, the restored insulation and the interface between the main insulation and the restored insulation; the thickness of the insulation sample is 0.2 mm; the process of measuring the average thickness includes measuring the thickness of at least five different positions of the insulation sample, and calculating the thickness of the insulation sample, and the calculation formula is as follows: Among them, d insul is the thickness of the insulating sample, d i is the thickness of the insulating sample obtained by the i-th measurement, and N is the number of measurements.

3. The method for calculating the spatial charge distribution of the cable factory joint at different temperatures according to claim 2 is characterized by: In step 2, the process of measuring the conductance current at different temperatures by the three-electrode method includes placing the insulating sample on the three-electrode structure, setting the test field strength to 40-60 MV / m, and controlling the test temperature to 20°C, 30°C, 40°C, 50°C, 60°C, 70°C, and 80°C; waiting for the internal charge of the insulating sample to completely dissipate and the temperature to stabilize, performing a polarization operation for 20-40 minutes and a depolarization operation for 5-15 minutes on the insulating sample, and taking the average value of the last 20-40 data points in the polarization process as the measured value of the conductance current.

4. The method for calculating the spatial charge distribution of the cable factory joint at different temperatures according to claim 3 is characterized by: The field strength is 50 MV / m, and the test temperature is controlled at 30°C, 50°C, and 70°C; the polarization operation time is 30 minutes, the depolarization operation time is 10 minutes, and the average value of the last 30 data points in the polarization process is taken as the measured value of the conductance current.

5. The method for calculating the spatial charge distribution of the cable factory joint at different temperatures according to claim 4 is characterized by: In step 2, based on the average thickness and the conductance current, the conductance current is divided by the contact area between the conductivity test electrode and the insulating sample to obtain the conductance current density. The calculation formula for the carrier mobility of the different insulating samples is as follows: Where μ is the carrier mobility of the insulating sample, J is the current density measured by the three-electrode method, ε0 is the vacuum dielectric constant, and ε r is the relative dielectric constant, V is the voltage amplitude applied to the insulating sample; The carrier mobility of different insulating samples at different temperatures is fitted, and the fitting formula for the relationship between temperature and the carrier mobility of the insulating sample is as follows: Where μ0 and E a are all constants obtained in the function fitting process, B is the Boltzmann constant, and T is the test temperature of the three-electrode method.

6. The method for calculating the spatial charge distribution of the cable factory joint at different temperatures according to claim 1 is characterized by: In step three, the process of testing the isothermal surface potential decay curve of the insulating sample after positive pressure charging and negative pressure charging includes placing the insulating sample flat on the ground electrode, keeping the distance between the voltage equalizing network and the insulating sample, and the distance between the voltage equalizing network and the needle electrode consistent, and controlling the test temperature to 20°C, 30°C, 40°C, 50°C, 60°C, 70°C, and 80°C; charging the insulating sample at negative pressure, the voltage applied to the needle electrode is -10 to -5kV, the voltage applied to the voltage equalizing network is -6 to -2kV, and the charging time is 2 to 4min; when the insulating sample is positively charged, the voltage applied to the needle electrode is 5 to 10kV, the voltage applied to the voltage equalizing network is 2 to 4kV, and the charging time is 2 to 4min; recording the isothermal surface potential decay curve of the insulating sample within 5s after the charging is completed, and the recording time is 30 to 50min.

7. The method for calculating the spatial charge distribution of the cable factory joint at different temperatures according to claim 6 is characterized by: The hole trap energy level and the electron trap energy level are calculated according to the test time and test temperature of the isothermal surface potential decay curve under positive pressure charging and negative pressure charging, respectively, and the calculation formula is as follows: In the formula, E T is the trap energy level, h is the Planck constant, T SPD is the test temperature of the isothermal surface potential decay curve, v is the vibration frequency of the molecules inside the insulating sample, and t is the time; The hole trap density and the electron trap density are calculated by differentiating the isothermal surface potential decay curves under positive pressure charging and negative pressure charging, respectively, and the calculation formula is as follows: In the formula, Q s (t) is the trap density, V(t) is the isothermal surface potential decay curve of the insulating sample over time, q e is the charge of the electron.

8. The method for calculating the spatial charge distribution of the cable factory joint at different temperatures according to claim 7 is characterized by: In step 4, the process of setting the boundary conditions includes: Set the boundary conditions of the bulk insulation close to the conductor side and calculate the current density of hole injection and electron extraction. The formula is as follows: In the formula, j h (r0, z0, t) and j e (r0, z0, t) are the current densities of hole injection and electron extraction on the conductor side of the bulk insulation, respectively. T(r0, z0, t) is the temperature of the bulk insulation of the cable factory connector on the conductor side. E(r0, z0, t) represents the electric field strength at time t in the r, z coordinate system. A is the Richard constant, k is the Boltzmann constant, and w hi and w ei The injection barrier for electrons and holes, e is the charge of a single charge, C e is the electron extraction coefficient, n eμ (r0, z0, t) is the charge density of the free electron eμ, μ e is the electron carrier mobility obtained by the three-electrode method, ε is the dielectric constant of the insulating sample; Set the boundary conditions at the interface between the bulk insulation and the restoration insulation, and the current density at the interface between the bulk insulation and the restoration insulation. The formula is as follows: Among them, j h (r, z, t) is the current density of holes at the interface between bulk insulation and recovery insulation, μ h is the hole carrier mobility, C ih is the barrier coefficient of the interface between the bulk insulation and the recovery insulation for holes, n hμ (r, z, t) is the charge density of the free hole hμ, j e (r, z, t) is the current density of electrons at the interface between bulk insulation and recovery insulation, μ e is the electron carrier mobility, C ie is the barrier coefficient of the interface between bulk insulation and recovery insulation for electrons, n eμ (r, z, t) is the charge density of free electrons eμ; Set the boundary conditions of the recovery insulation close to the outer shield side and calculate the current density of hole extraction and electron injection. The formula is as follows: Among them, j e (r d , z d , t) and j h (r d , z d , t) are the current densities of electron injection and hole extraction near the outer shielding side of the recovery insulation, T(r d , z d , t) is the temperature of the cable factory joint where the insulation is restored near the outer shield side, E(r d , z d , t) represents the electric field intensity at time t in the r, z coordinate system, C h is the extraction coefficient of the hole, n eμ (r d , z d , t) is the charge density of free holes hμ, μ h is the hole carrier mobility obtained by the three-electrode method.

9. The method for calculating the spatial charge distribution of cable factory joints at different temperatures according to claim 1, characterized in that: In step 4, based on the carrier mobility, electron trap energy level, electron trap density, hole trap energy level and hole trap density of different insulating samples, the formula of the cable factory joint bipolar carrier model is as follows: Wherein, the subscript a represents different types of carriers, which can be divided into free electrons eμ, trapped electrons et, free holes hμ, and trapped holes ht; ja(r, z, t) represents the current density of carrier a at time t in the r, z coordinate system; μ a is the carrier mobility of carrier a; n a (r, z, t) represents the charge density of carrier a at time t in the r, z coordinate system; D fa represents the escape coefficient; E(r, z, t) represents the electric field intensity at time t in the r, z coordinate system, ρ(r, z, t) represents the volume charge density at time t in the r, z coordinate system; S a (r, z, t) represents the process of interaction between different carriers at time t in the r, z coordinate system, which is called the source phase.

10. The method for calculating the spatial charge distribution of the cable factory joint at different temperatures according to claim 9, characterized in that: In step 5, the electron and hole trap parameters at different insulation positions are substituted into the source phase to calculate the spatial charge distribution inside the cable factory joint. The calculation method is shown in the formula: Among them, S0, S1, S2 and S3 are composite coefficients, B h and Be is the trap coefficient, n oet and n oht are the electron trap density and hole trap density calculated from the surface charge decay curve, D h and D e are the trapping coefficients of holes and electrons, which are positively correlated with the trap energy levels calculated from the surface charge decay curve, and s ht 、s hμ 、s et and eμ It is the source phase of free electrons eμ, trapped electrons et, free holes hμ, and trapped holes ht.

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