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

Abstract

The application discloses a kind of calculation methods of space charge distribution of cable factory joint at different temperatures, comprising the following steps: step one: cutting sample of cable factory joint insulation sample, and measuring average thickness;Step two: measuring conductance current at different temperatures, calculating carrier mobility, and fitting temperature and insulation sample carrier mobility;Step three: test positive pressure and negative pressure charging isothermal surface potential decay curve, obtain electron trap energy level, electron trap density, hole trap energy level and hole trap density at different temperatures;Step four: set boundary condition, establish bipolar carrier model;Step five: carrier mobility, electron trap energy level, electron trap density, hole trap energy level and hole trap density are substituted into bipolar carrier model, and space charge distribution is obtained.The application can quickly and accurately calculate the space charge distribution in the interior of cable factory joint, reduce the risk of failure caused by unreasonable space charge distribution.

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 cable factory joints at different temperatures. Background Art

[0002] Currently, the proportion of renewable energy generation in the power system is increasing. Offshore wind power, with its abundant resources and high power generation hours, is experiencing significant development. High-capacity ultra-high voltage DC submarine cables, insulated with cross-linked polyethylene (XLPE), are widely used in DC transmission applications such as offshore wind power, offshore photovoltaic power generation, and long-distance cross-sea transmission, thanks to their simple manufacturing process and high transmission capacity.

[0003] During the production process of factory joints, it is necessary to inject newly melted XLPE into the insulation of the submarine cable body that has been polished into a cone, and then form the recovery insulation after high-temperature and high-pressure vulcanization. Since the body insulation is subjected to two high-temperature and high-pressure vulcanizations, and the recovery insulation is only subjected to one, there will be an interface between the body insulation and the recovery insulation. The difference in carrier transport speed and trap distribution on both sides of the interface can easily cause space charge accumulation at and around the interface, accelerate material aging, and ultimately cause insulation failure. The existing method for calculating the spatial charge distribution of cable insulation performance at different temperatures is not accurate enough and the calculation speed is slow. In addition, there is a lack of comprehensive consideration and accurate quantitative calculation methods for the relationship between the complex carrier behavior inside the cable joint, including 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 this invention is to provide a method for calculating the space charge distribution of cable factory joints at different temperatures. The present invention can quickly and accurately calculate the space charge distribution inside the cable factory joints, reducing the risk of failure caused by unreasonable space 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 into an insulation sample using the ring cutting method, and measure the average thickness of the insulation sample;

[0007] Step 2: Use the three-electrode method to measure the conductivity current of the insulating sample at different temperatures. Based on the average thickness and conductivity current, calculate the carrier mobility of different insulating samples, and fit the relationship between temperature and carrier mobility of the insulating sample;

[0008] Step 3: Measure the isothermal surface potential decay curves of the insulating sample after positive pressure charging and negative pressure charging, and use the isothermal surface potential decay curves 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 connectors 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 using the cable factory joint bipolar carrier model.

[0011] 3. In the aforementioned method for calculating the spatial charge distribution of cable factory joints at different temperatures, in step 1, the ring cutting sampling locations 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 average thickness measurement process includes measuring the thickness of the insulation sample at at least five different locations, and calculating the thickness of the insulation sample using the following formula:

[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 40-60 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 of the last 20-40 data points of 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 50 MV / m, and the test temperature is controlled at 30°C, 50°C, and 70°C; the polarization operation time is 30 minutes, and the depolarization operation time is 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.

[0016] In the aforementioned method for calculating the spatial charge distribution of cable factory joints at different temperatures, in step 2, based on the average thickness and 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 specimen;

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

[0020]

[0021] Where μ0 and E a are constants obtained during 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 balancing network and the insulating sample, and the voltage balancing 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 balancing 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 balancing network is 2 to 4kV, and the charging time is 2 to 4min; and recording the isothermal surface potential decay curve of the insulating sample within 5s after the end of charging, and the recording time is 30 to 50min.

[0023] In the aforementioned method for calculating the space charge distribution of the cable factory joint at different temperatures, the hole trap energy level and the electron trap energy level are calculated based on 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:

[0024]

[0025] Where, 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 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] Where 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 on the conductor side of the bulk insulation to calculate the current density of hole injection and electron extraction. The formula is as follows:

[0031]

[0032] Where, 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 of 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 layer for holes, n hμ (r, z, t) is the charge density of free holes 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 the free electron 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 on the side of the recovery insulation close to the outer shield, 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 hole extraction coefficient, 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 space 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 cable factory joint bipolar carrier model is as follows:

[0040]

[0041] Among them, 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 for the space charge distribution of the cable factory joint at different temperatures, in step 5, the electron and hole trap parameters at different insulation positions are substituted into the source phase to calculate the space 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 hole and electron detrapping coefficients, which are positively correlated with the trap energy levels calculated from the surface charge decay curve, and s ht 、S hμ 、s et and s 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 a bipolar carrier model of the cable factory joint by setting boundary conditions. Then, according to the model, the spatial charge distribution inside the cable factory joint is quickly and accurately calculated, which can more accurately evaluate the performance of the cable factory joint under different operating temperature environments, help 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 spatial charge distribution. In addition, the present invention can help scientific researchers intuitively analyze the accumulation of spatial charge inside the cable factory joint under actual working conditions, discover weak positions 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 This is a flow chart for calculating the spatial charge distribution at different temperatures of the cable factory joint 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 This is the spatial charge distribution of the cable factory joint at different temperatures of the present invention. DETAILED DESCRIPTION

[0051] The present invention will be further described below with reference to the accompanying drawings and examples, but they are not intended to limit the present invention.

[0052] Example: A method for calculating the space 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 into an insulation sample using the ring cutting method, and measure the average thickness of the insulation sample;

[0054] In step one, if Figure 2The figure below shows a schematic diagram of the cable factory joint ring cutting process. Place the cable factory joint sample on a lathe, place the cutter against the outside of the cable factory joint sample, and rotate the cable factory joint sample to begin ring cutting. The distance between the cutter and the cable factory joint sample is controlled to ensure the sample thickness is approximately 0.2 mm. The factory joint insulation is divided into three parts: bulk insulation, recovery insulation, and the interface between bulk insulation and recovery insulation. Insulation specimens for these three parts are prepared based on the sample locations during ring cutting.

[0055] In this embodiment, the insulation sample is cut into a 5 cm x 5 cm sheet after circular cutting. The insulation sample is cleaned for 2 minutes using an ultrasonic cleaner, and both sides of the cleaned insulation sample are wiped to ensure that no dirt remains. The thickness of the insulation sample is measured at at least five different locations using a thickness gauge with an accuracy of at least 0.001 mm. The thickness of the insulation sample is calculated using the following formula:

[0056]

[0057] Among them, d insul is the thickness of the insulating sample, d i is the thickness of the insulation sample obtained by the i-th measurement, and N is the number of measurements. The calculated average thicknesses of different insulation samples are shown in Table 1.

[0058] Table 1 Average thickness of different insulation samples

[0059]

[0060] Step 2: Use the three-electrode method to measure the conductivity current of the insulating sample at different temperatures. Based on the average thickness and conductivity current, calculate the carrier mobility of different insulating samples, and fit the relationship between temperature and carrier mobility of the insulating sample;

[0061] In this example, an insulating sample is placed on a three-electrode structure. The measuring electrode and high-voltage electrode in the three-electrode structure are stainless steel cylinders with diameters of 3 cm and 4.5 cm, respectively. The measuring electrodes are surrounded by ring electrodes 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 with a test field strength of 50 MV / m. The oven controls the test temperatures to 30, 50, and 70°C. During testing, the sample is placed in the equipment for at least one hour to allow the internal charge to completely dissipate and the temperature to stabilize. The sample is then polarized for 30 minutes and depolarized for 10 minutes. The average of the final 30 data points during the polarization process is used as the measured 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 carrier mobility of insulating samples is obtained as follows:

[0066]

[0067] Where μ0 and E a are constants obtained during 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 distances between the voltage balancing network and the sample to be tested, as well as between the voltage balancing network and the needle electrode, should remain constant. During the isothermal surface potential decay curve test, the ambient temperature and humidity should remain constant, with the humidity maintained 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 conductivity and current, which is 30, 50, and 70°C.

[0073] During negative pressure charging experiments, the voltage applied to the needle electrode was -8kV, the voltage applied to the voltage balancing network was -4kV, and the charging time was 3 minutes. During positive pressure charging experiments, the voltage applied to the needle electrode was 8kV, the voltage applied to the voltage balancing network was 4kV, and the charging time was 3 minutes. After charging, the sample should be moved under the potentiometer within 5 seconds to record the decay of the surface potential for 40 minutes.

[0074] The hole trap energy level and electron trap energy level are calculated based on 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] Where, 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 and negative pressure charging, respectively. The calculation formula is as follows:

[0078]

[0079] Where 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 of different insulating samples at different temperatures

[0084]

[0085]

[0086] Step 4: Set boundary conditions and establish a bipolar carrier model for cable factory connectors 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 on the conductor side of the bulk insulation to calculate the current density of hole injection and electron extraction. The formula is as follows:

[0089]

[0090] Where, 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, 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, w hi and w ei The injection barrier of 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 layer for holes, n hμ (r, z, t) is the charge density of free holes 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 the free electron 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 on the side of the recovery insulation close to the outer shield, 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 hole extraction coefficient, 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 using 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 mobility in the bulk insulation, the interface between the bulk insulation and the recovery insulation, and the recovery insulation is calculated using the transport equation, Poisson's equation, and the continuity equation. The formula for the bipolar carrier model of the cable factory joint is as follows:

[0099]

[0100] Among them, 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 space 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 hole and electron detrapping coefficients, which are positively correlated with the trap energy levels calculated from the surface charge decay curve, and s ht 、S hμ 、s et and s 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 insulation samples at different insulation positions at 30℃, 50℃ and 70℃, the internal space charge distribution of the cable factory joints under different conditions is calculated. Figure 4 The maximum space charge density and maximum electric field distortion at different temperatures inside the cable factory connector 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 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, as the temperature increases, the space charge accumulation becomes more serious, and the root of the stress cone can easily 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 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 a bipolar carrier model of the cable factory joint. Subsequently, the distribution change of the space charge inside the factory joint with the change of pressurization time can be evaluated according to the model, which can more accurately evaluate the performance of the cable factory joint under different working temperature environments, help 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 positions inside the cable factory joint in advance, and provide cable manufacturers with scientific analysis means for the design and development of ultra-high voltage submarine cable factory joints.

[0108] In summary, the present invention can quickly and accurately calculate the space charge distribution inside the cable factory joint, reducing the risk of failure caused by unreasonable space 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 into an insulation sample using the ring cutting method, and measure the average thickness of the insulation sample; Step 2: Use the three-electrode method to measure the conductivity current of the insulating sample at different temperatures. Based on the average thickness and conductivity current, calculate the carrier mobility of different insulating samples, and fit the relationship between temperature and carrier mobility of the insulating sample; Step 3: Measure the isothermal surface potential decay curves of the insulating sample after positive pressure charging and negative pressure charging, and use the isothermal surface potential decay curves 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 connectors 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 using the cable factory joint bipolar carrier model.

2. The method for calculating the spatial charge distribution of cable factory joints at different temperatures according to claim 1 is characterized by: In step 1, the locations of the ring cutting method are the bulk insulation, the restored insulation, and the interface between the bulk 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 locations of the insulation sample and calculating the thickness of the insulation sample. The calculation formula is as follows: ； in, is the thickness of the insulating specimen, For the The thickness of the insulation sample obtained by the measurement, is the number of measurements.

3. The method for calculating the spatial charge distribution of cable factory joints 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 of the last 20-40 data points of the polarization process as the measured value of the conductance current.

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

5. The method for calculating the spatial charge distribution of cable factory joints 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, is the carrier mobility of the insulating sample, is the current density measured by the three-electrode method, is the dielectric constant of vacuum, is the relative dielectric constant, is the voltage amplitude applied to the insulation specimen; The carrier mobility of different insulating samples at different temperatures is fitted, and the fitting formula for the relationship between temperature and carrier mobility of insulating samples is obtained as follows: ； Where, and are all constants obtained during the function fitting process. is the Boltzmann constant, is the test temperature of the three-electrode method.

6. The method for calculating the spatial charge distribution of cable factory joints 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 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; the insulating sample is negatively charged, the voltage applied to the needle electrode is -10~-5kV, the voltage applied to the voltage equalizing network is -6~-2kV, and the charging time is 2~4min; when the insulating sample is positively charged, the voltage applied to the needle electrode is 5~10kV, the voltage applied to the voltage equalizing network is 2~4kV, and the charging time is 2~4min; the isothermal surface potential decay curve of the insulating sample is recorded within 5s after the end of charging, and the recording time is 30~50min.

7. The method for calculating the spatial charge distribution of a cable factory joint at different temperatures according to claim 6, characterized in that: The hole trap energy level and electron trap energy level are calculated based on the test time and test temperature of the isothermal surface potential decay curves under positive pressure charging and negative pressure charging, respectively, and the calculation formula is as follows: ； Where, is the trap level, is the Boltzmann constant, is Planck's constant, is the test temperature of the isothermal surface potential decay curve, is the vibration frequency of the molecules inside the insulating sample, For time; 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, and the calculation formula is as follows: ； Where, is the trap density, is the dielectric constant of vacuum, is the relative dielectric constant, is the thickness of the insulating specimen, is the isothermal surface potential decay curve of the insulating sample over time, is the charge of the electron.

8. The method for calculating the spatial charge distribution of a cable factory joint at different temperatures according to claim 7, characterized in that: In step 4, the process of setting the boundary conditions includes: Set the boundary conditions on the conductor side of the bulk insulation to calculate the current density of hole injection and electron extraction. The formula is as follows: ； Where, and are the current densities of hole injection and electron extraction on the conductor side of the bulk insulation, It is the temperature of the insulation of the cable factory connector body close to the conductor side. Representatives in In the coordinate system The electric field strength at the moment, is the Richard constant, is the Boltzmann constant, and The electron and hole injection barriers, is the charge of a single charge, is the electron extraction coefficient, Free electrons The charge density, To obtain the electron carrier mobility by the three-electrode method, 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: ； in, is the current density of holes at the interface between bulk insulation and recovery insulation, is the hole carrier mobility, is the barrier coefficient of the interface between the bulk insulation and the recovery insulation layer for holes, Free holes The charge density, is the current density of electrons at the interface between bulk insulation and recovery insulation, is the electron carrier mobility, is the barrier coefficient of the interface between bulk insulation and recovery insulation for electrons, Free electrons The charge density of 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: ； in, and are the current densities of electron injection and hole extraction on the side of the insulation restoration shield, It is the temperature at the cable factory joint where the insulation is restored close to the outer shield side. Representatives in In the coordinate system The electric field strength at the moment, is the hole extraction coefficient, Free holes The charge density, is the hole carrier mobility obtained by the three-electrode method.

9. The method for calculating the spatial charge distribution of a cable factory joint 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: ； Among them, the subscript Represents different types of carriers, specifically free electrons , trapped electrons , free holes , trapped holes ; Representatives in In the coordinate system Moment carrier The current density; For carriers The carrier mobility of Representatives in In the coordinate system, Moment carrier The charge density of represents the coefficient of debonding; Representatives in In the coordinate system The electric field strength at the moment, Representatives in In the coordinate system The volume charge density at time t; Representatives in In the coordinate system The process in which carriers at different times interact with each other is called the source phase.

10. The method for calculating the spatial charge distribution of a 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 space charge distribution inside the cable factory joint. The calculation method is shown in the formula: ； in, 、 、 and is the composite coefficient, and is the trap coefficient, and are the electron trap density and hole trap density calculated from the surface charge decay curve, and 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 Free electrons , trapped electrons , free holes , trapped holes The source phase.

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