A method and apparatus for simulating dynamic development of internal degradation defects of a cable joint

Abstract

A kind of dynamic development process simulation method and device of internal deterioration defect of cable joint, method includes: the finite element composite model of internal electric-thermal field of cable joint including internal deterioration defect area is established;The finite element composite model is solved based on preset initial operating condition, and the real-time distribution of electric field intensity and temperature in cable joint is obtained;According to the distribution of electric field intensity and temperature at current time, material parameters at internal deterioration defect area are corrected in real time;Based on the distribution of electric field intensity and temperature at current time and the material parameters of correction, the finite element composite model is solved again, to update the distribution of electric field intensity and temperature at next time;The steps of real-time correction and re-solution are repeated until the iteration termination condition is satisfied.The whole deterioration dynamic process temperature distribution and thermal breakdown time temperature of internal deterioration defect of cable joint can be obtained by the present application, which provides basis for internal defect detection and early warning of cable head.

Description

Technical Field

[0001] This invention belongs to the field of high voltage and insulation, online monitoring and fault diagnosis of power equipment, and particularly relates to a method and device for simulating the dynamic development process of internal deterioration defects in cable joints. Background Technology

[0002] Cable joints are among the weakest links in a cable system. Due to factors such as construction defects, joint oxidation, loose crimping, inconsistent installation quality, and poor operation and maintenance, cable joints are prone to various defects, such as scratches on the main insulation, uneven semiconductor layers, and air gaps. These defects can lead to distortion of the electric field strength, which in turn can cause partial discharge, accelerate the aging of the cable joint insulation, and even cause the cable operating temperature to rise, affecting the cable's current carrying capacity and potentially leading to cable accidents. Therefore, simulation studies of internal degradation defects in cable joints are of great significance.

[0003] Domestic and international research institutions have conducted extensive research on simulation calculations of internal degradation defects in cable joints. The main techniques used are as follows: (1) Application of finite element simulation technology: At present, the finite element analysis method is widely used in the study of electrothermal simulation of internal defects in cable joints. Researchers can establish a refined model of the cable joint, such as a model containing air wedge gap defects of different sizes for the intermediate joint of a 35kV power cable, and calculate the electric field and temperature distribution under different operating conditions to explore the impact of defects on the performance of the cable joint.

[0004] (2) Multiphysics coupling analysis: Considering the mutual coupling relationship between the electric field and temperature field inside the cable joint, many studies have focused on the simulation analysis of thermoelectric coupling fields. For example, the ANSYS finite element software was used to simulate the thermoelectric coupling field inside a 220kV cable joint. The thermoelectric field distribution characteristics were studied when there were defects such as impurity particles in the insulation material, burrs on the surface of the stress cone, and aging of the internal insulation material. It was found that these defects would lead to higher structural temperatures and affect the thermoelectric performance of the joint.

[0005] (3) Analysis of defect types: Studies were conducted on various common internal defects of cable joints, including scratches on the main insulation, inclusion of impurities and particles, misalignment of stress cones, uneven peeling of the semiconductive layer, and burrs on the connecting pipe. For example, Fang Chunhua et al.'s "Simulation Analysis of Typical Defects in 10kV Cable Intermediate Joints" conducted electric field simulation analysis on four typical construction defects of 10kV cable intermediate joints: scratches on the main insulation, impurities in the main insulation, burrs on the connecting pipe, and uneven peeling of the semiconductive layer, and determined the electric field distortion rate around each typical defect.

[0006] However, during operation, the electric field, temperature field, and defect state within a cable joint are not static but dynamically change with time, load variations, and other factors. Current simulation studies mostly focus on static or steady-state analysis, insufficiently considering the dynamic characteristics of the cable's internal structure. This makes it difficult to accurately describe the development and evolution of defects under dynamic operating conditions and their long-term impact on cable joint performance, thus hindering the provision of accurate early warning signals. Furthermore, considering dynamic characteristics could drastically increase the complexity of finite element simulations, potentially leading to slow or non-convergence in some cases, thus affecting computational efficiency and the reliability of the results. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention aims to provide a simulation method and apparatus for the dynamic development process of internal deterioration defects in cable joints. This method ensures simulation efficiency while considering the dynamic characteristics of internal deterioration in cable joints, enabling accurate simulation of the development and evolution of defects under dynamic operating conditions. Consequently, it can accurately predict the temperature distribution and thermal breakdown temperature during the entire deterioration process, providing an important basis for the detection and early warning of internal defects in cable heads.

[0008] According to a first aspect of the present invention, a simulation method for the dynamic development process of internal degradation defects in cable joints is provided. The method includes the following steps: A finite element composite model of the internal electrothermal field of the cable joint, including the internal deterioration defect region, was established. The finite element composite model is solved based on the preset initial working conditions to obtain the real-time distribution of electric field intensity and temperature inside the cable joint. Based on the current distribution of electric field intensity and temperature, the conductivity at the internal deterioration defect region is corrected in real time. Based on the corrected conductivity and the current distribution of electric field intensity and temperature, the finite element composite model is re-solved to update the distribution of electric field intensity and temperature at the next moment. The process involves iteratively performing real-time corrections and resolving the problem to obtain the temperature distribution at each iteration time, until the iteration termination condition is determined.

[0009] Furthermore, the real-time correction of conductivity at the internal degradation defect region includes: Traverse each grid cell within the internal degradation defect region, obtain the electric field intensity and temperature of the corresponding grid cell at the current moment, and calculate the target conductivity of each grid cell for the current iteration based on the preset conductivity model, as the corrected conductivity.

[0010] Furthermore, the preset conductivity model is as follows:

[0011] in, For the corresponding grid cell i In the current iteration k The target conductivity is as follows. For the corresponding grid cell i In the current iteration k electric field strength under, For the corresponding grid cell i In the current iteration k temperature, A , B , C These are the first, second, and third empirical coefficients, respectively.

[0012] Furthermore, the real-time correction of conductivity at the internal deterioration defect region also includes: Determine the absolute value of the ratio of the difference between the target conductivity and the preset conductivity of each grid cell in the current iteration to the preset conductivity; The largest absolute value of the ratio is selected from the absolute values ​​of the ratios of each grid cell and used as the relative rate of change of conductivity of the internal deterioration defect region in the current iteration. The relative rate of change of conductivity is compared with preset upper and lower thresholds of the rate of change, and the time step of the next iteration is determined based on the comparison results. The corrected conductivity and the time step for the next iteration are passed to the finite element composite model.

[0013] Further, the relative rate of change of conductivity is compared with preset upper and lower thresholds for the rate of change, and the time step for the next iteration is determined based on the comparison result, including: When the relative rate of change of conductivity exceeds a preset upper limit threshold, the time step of the current iteration is adjusted. Multiply by reduction factor As the time step for the next iteration ;in, , To reduce the lower limit of the factor, To preset the upper limit of the rate of change of conductivity, For the current iteration k The relative rate of change of conductivity; When the relative rate of change of conductivity is less than a preset lower limit threshold, the time step of the current iteration is adjusted. Multiply by the recovery factor As the time step for the next iteration ;in, , This is the upper limit of the recovery factor. The lower limit of the preset rate of change of conductivity; When the relative rate of change of conductivity is between the preset upper limit threshold and the preset lower limit threshold: the time step of the current iteration is used as the time step of the next iteration.

[0014] Furthermore, the relative rate of change of conductivity of the corresponding grid in the current iteration is calculated as follows:

[0015] in, This refers to the set of mesh cells within the internal degradation defect region. For the corresponding grid cell i In the current iteration k The relative rate of change of conductivity under the following conditions For the corresponding grid cell i In the current iteration k The conductivity value below, For the corresponding grid cell i In the current iteration k The target conductivity value is set below.

[0016] Further, determining the arrival of the iteration termination condition includes: It is determined that the temperature of the internal deterioration defect area exceeds a preset temperature threshold; or The internal deterioration defect area was determined to have reached thermal equilibrium.

[0017] Furthermore, the method of the present invention also includes: After determining that the maximum temperature of each grid cell in the internal deterioration defect region exceeds a preset temperature threshold, the grid cell corresponding to the maximum temperature is determined, and the second derivative of temperature with respect to time for that grid cell is calculated in each iteration. In each iteration of the grid cell, when the ratio of the second derivative value of each iteration to the value of the previous iteration exceeds a preset ratio threshold in the first consecutive m iterations, the temperature corresponding to the first iteration in the first consecutive m iterations is determined as the thermal breakdown critical temperature; where m is an integer greater than or equal to 3.

[0018] According to a second aspect of the present invention, a simulation device for the dynamic development process of internal degradation defects in cable joints using the method described in the first aspect of the present invention is provided. The device includes: The modeling module is used to create a finite element composite model of the internal electrothermal field of the cable joint, including the internal deterioration and defect area. The initial solution module is used to solve the finite element composite model based on preset initial working conditions to obtain the real-time distribution of electric field intensity and temperature inside the cable joint. The correction module is used to correct the material parameters at the internal deterioration defect area in real time based on the current electric field strength and temperature distribution. The update module is used to re-solve the finite element composite model based on the corrected material parameters and the current electric field intensity and temperature distribution, so as to update the electric field intensity and temperature distribution at the next moment. The iterative module is used to repeat the steps of real-time correction and resolving until the iteration termination condition is met.

[0019] According to a third aspect of the present invention, a terminal is provided. The terminal includes a processor and a storage medium: the storage medium is used to store instructions; the processor is used to operate according to the instructions to perform the steps of the method according to the first aspect of the present invention.

[0020] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: 1. This method overcomes the limitations of traditional simulations that set material parameters to constant values. In each iteration, it updates the conductivity parameters at the internal degradation defect region in real time based on the current electric field strength and temperature distribution. This dynamic feedback mechanism accurately simulates the nonlinear growth process of conductivity in the defect region with temperature and electric field changes, thus realistically reproducing the complete physical evolution of defects from slow development to rapid degradation. It effectively obtains the temperature distribution throughout the entire degradation dynamic process of internal degradation defects in cable joints, resulting in simulation results that more closely resemble actual operating conditions.

[0021] 2. A pre-defined conductivity model with electric field strength and temperature as bivariates was adopted to calculate the target conductivity. The exponential function accurately characterizes the nonlinear growth characteristics of the insulating material's conductivity. The exponential function can sensitively capture the rapid increase in conductivity in the defect region caused by electric field distortion and local overheating. The bivariate model simultaneously reflects the synergistic amplification effect of increased electric field and temperature on conductivity, avoiding the deficiency of univariate models in underestimating the conductivity growth rate under strong electric field and high-temperature coupling scenarios. Compared to linear or power function models, this model more realistically reproduces the nonlinear dynamic characteristics of the entire process from slow degradation to accelerated thermal runaway of the defect.

[0022] 3. By calculating the relative rate of change of conductivity in adjacent iterations of the defect region, the system automatically determines its current evolution stage and adaptively adjusts the iteration time step accordingly. When conductivity changes drastically, synchronously reducing the time step can reduce the disturbance amplitude of a single iteration, effectively solving the numerical divergence problem caused by exponential changes in conductivity during thermal runaway. When conductivity changes gradually, the time step is gradually restored to avoid computational efficiency loss caused by conservative parameters throughout the process, achieving a balance between simulation accuracy and computational efficiency.

[0023] 4. By analyzing the second derivative behavior of the maximum temperature in the defect area with respect to time, the thermal runaway (thermal breakdown) inflection point can be automatically identified during the simulation process, thereby achieving an accurate estimate of the temperature at the moment of thermal breakdown, providing an important basis for the detection and early warning of internal defects in cable heads. Attached Figure Description

[0024] Figure 1 This is an overall flowchart of a simulation method for the dynamic development process of internal deterioration defects in a cable joint, as described in one embodiment of the present invention. Figure 2 This is a flowchart illustrating the simulation method for the dynamic development process of internal deterioration defects in cable joints in this embodiment of the present invention. Figure 3 This is a schematic diagram of the geometric model of the cable connector in this embodiment; Figure 4 This is a schematic diagram of the mesh generation results in this embodiment; Figure 5 This is a schematic diagram of the thermal field calculation results for critical thermal breakdown in this embodiment. Detailed Implementation

[0025] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0026] It should be noted that in this invention, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Without further limitations, an element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0027] Cable joints are among the weakest links in a cable system. Construction defects, oxidation, and loose crimping can easily lead to defects such as scratches on the main insulation, uneven semiconductor layers, and air gaps. These defects can cause distortion of the electric field strength, resulting in partial discharge, accelerated insulation aging, and even increased operating temperature, potentially leading to accidents. However, traditional finite element simulations mostly focus on static or steady-state analysis, assuming constant material conductivity, which fails to reflect the evolution of material parameters under thermo-electric coupling effects. Furthermore, even considering that temperature changes affect key material parameters, temperature changes are nonlinear. In strongly nonlinear scenarios, considering temperature changes may result in slow convergence or even non-convergence, or lead to oscillations or divergences in the solution due to abrupt parameter changes, thus failing to fully simulate the entire process from slow defect development to thermal breakdown.

[0028] Therefore, this invention aims to provide a simulation method and apparatus for the dynamic development process of internal degradation defects in cable joints. Addressing the shortcomings of existing technologies that fail to adequately consider dynamic characteristics and accurately describe the evolution of defects under dynamic operating conditions, this invention solves the aforementioned problems from both physical mechanism and numerical method perspectives by introducing differentiated material modeling, real-time grid-by-grid conductivity correction, and adaptive time step control based on the relative rate of change of conductivity. This achieves accurate simulation of the entire process of internal degradation defects in cable joints, from slow development to thermal breakdown. The method is described in detail below with reference to the accompanying drawings.

[0029] According to a first aspect of the present invention, a method for simulating the dynamic development process of internal degradation defects in a cable is provided.

[0030] like Figure 1 As shown, in one embodiment, the method for calculating the dynamic development process of internal degradation defects in the cable includes the following steps: Step S1: Establish a finite element composite model of the internal electrothermal field of the cable joint, including the internal deterioration defect area.

[0031] Specifically, the steps include: Step S11: Establish a geometric model of the cable joint based on its actual physical structure.

[0032] In this step, the first step is to open the finite element software and create a new geometric model. For example, for a cable joint, the geometric model can be set to include conductor layers, insulation layers, and internal defects, and parameters such as the geometric dimensions, shape, and material properties of the conductor layers, insulation layers, and internal defects can be set to ensure that the model can accurately reflect the actual physical structure and physical properties.

[0033] The geometric dimensions and shapes of the various structures involved in the geometric model in this implementation case are as follows: Figure 3 As shown.

[0034] When setting material properties, it is necessary to define the thermophysical properties of the conductor layer and the insulating layer, such as thermal conductivity, specific heat capacity, electrical conductivity, and density. These material parameters can be selected from the material library or set based on experimental data.

[0035] Furthermore, based on extensive experimental research, this invention has found that the conductivity change in the internal deterioration defect region is significantly greater than that in other conductor or insulation layers as the internal electric field strength and temperature of the cable joint change. Therefore, based on these findings, the material properties of the conductor and insulation layers can be considered essentially constant, unaffected by electric field strength and temperature; thus, these material properties can be selected from a material library. However, the material properties in the internal deterioration defect region are considered to be greatly influenced by electric field strength and temperature and should be set as variables. Therefore, this invention proposes incorporating the characteristic of conductivity changing with the electric field into existing finite element simulation software. Specifically, this invention employs a differentiated material parameter assignment strategy: for normal regions outside the internal deterioration defect region, constant material parameters are used to reduce model complexity and computational overhead; for the internal deterioration defect region, its conductivity will be dynamically corrected in subsequent iterations based on real-time electric field and temperature to accurately reflect the nonlinear evolution behavior of the material under electrothermal coupling (this process is achieved through co-simulation described later).

[0036] Step S12: Construct the heat transfer physical field of the cable joint.

[0037] This step generally includes: setting the corresponding convective boundary, convective heat transfer coefficient, and contact thermal resistance based on the actual thermal contact between the cable joint and the external air or other objects. For example, when the outer surface of the cable joint is in contact with air, the natural convection heat transfer coefficient can be set; if it is in thermal contact with other objects, the contact thermal resistance needs to be defined. The accurate setting of the heat transfer physical field is the basis for subsequent temperature distribution calculations and directly affects the simulation accuracy of heat accumulation and heat dissipation processes in defect areas. Step S13: Construct the current physical field of the cable joint.

[0038] This step generally includes setting the current source or voltage boundary conditions.

[0039] The current physical field is set up to simulate the load current in actual operation, accurately calculate the current distribution in the conductor and the resulting Joule heating. The selection of the current source or voltage boundary conditions should be determined based on the actual operating conditions of the cable joint.

[0040] After completing the above settings, mesh the finite element composite model. Figure 4The mesh generation results in this embodiment are shown. Mesh refinement is applied to the internal deterioration defect region and its adjacent regions to ensure sufficient solution accuracy in areas with drastic parameter gradient changes, while a coarser mesh is used in regions far from the defect, thus balancing computational accuracy with computational efficiency.

[0041] Step S14: Select a suitable solver to solve the heat transfer equation. Set parameters such as the solution time step and convergence criterion according to the nature of the problem (steady-state or transient). For transient problems, the initial temperature conditions need to be determined. Save the established finite element model for subsequent interaction with third-party calculation software.

[0042] Step S2: Solve the finite element composite model based on the preset initial working conditions to obtain the real-time distribution of electric field intensity and temperature inside the cable joint.

[0043] The initial operating conditions are set by the user in the finite element simulation software, including the initial ambient temperature, load current and voltage.

[0044] In this embodiment, the initial ambient temperature can be set to 25°C in the finite element software, and a rated operating current can be applied to the conductor. Based on these initial operating conditions, the finite element software performs an initial solution on the finite element composite model established in step S1, solving the coupled current continuity equation and heat conduction equation to obtain the electric field intensity distribution and temperature distribution of each mesh element at the initial moment. After the solution is completed, the finite element software saves the initial electric field and temperature distribution data for subsequent iterative correction. This step establishes the initial state of the entire dynamic simulation process, providing a starting benchmark for subsequent iterative corrections.

[0045] Step S3: Based on the current electric field strength and temperature distribution, the conductivity at the internal deterioration defect region is corrected in real time.

[0046] This is one of the core steps of this invention. Traditional methods typically set material parameters to constant values, while this invention uses real-time corrected conductivity in the defect region, enabling the simulation to dynamically track the evolution of material parameters. In a co-simulation architecture, this step is performed by third-party computational software. After the finite element software returns the electric field intensity and temperature distribution obtained at the current moment to the third-party software, the third-party software performs real-time correction of the conductivity according to the following sub-steps. This step further includes the following sub-steps: Step S31: Traverse each grid cell in the internal deterioration defect region, obtain the electric field intensity and temperature of the corresponding grid cell at the current moment, and calculate the target conductivity of each grid cell in the current iteration according to the preset conductivity model, as the corrected conductivity.

[0047] This conductivity model is based on the conductivity theory of solid insulating materials. The conductivity of insulating materials is mainly determined by the migration process of charge carriers (electrons and ions). Under the action of an applied electric field, charge carriers gain energy, and their migration process is affected by two main mechanisms: one is the effect of the electric field on the reduction of the charge carrier potential barrier (Poeux-Frankel effect), and the other is the effect of temperature on the thermal activation transition of charge carriers (Arrhenius thermal activation mechanism).

[0048] Regarding the effect of an electric field, according to the Purl-Frankel effect, under a strong electric field, the trapping barrier inside a material decreases due to the external electric field, and the conductivity has an exponential relationship with the square root of the electric field strength E, that is:

[0049] in For Purl-Frankel constant, Boltzmann's constant, T This refers to absolute temperature.

[0050] Regarding the effect of temperature, the thermally activated transitions of charge carriers follow the Arrhenius relation, and the relationship between conductivity and temperature can be expressed as:

[0051] in, It is the activation energy.

[0052] By coupling the electric field effect and the temperature effect, and simplifying the temperature coupling term for engineering applications, the bivariate exponential conductivity model of this invention is obtained:

[0053] in, For the corresponding grid cell i In the current iteration k The target conductivity is as follows. For the corresponding grid cell i In the current iteration k electric field strength under, For the corresponding grid cell i In the current iteration k The temperature is given by A, B, and C, which are the first, second, and third empirical coefficients, respectively. In one specific embodiment, A = 9.92 × 10⁻⁶, obtained by fitting experimental data. - ³, B = 1.287 × 10 - ³, C = 1.01 × 10 4 .

[0054] In the exponential term of the aforementioned preset conductivity model, Originating from the Purl-Frankel effect, it reflects the effect of the electric field on lowering the potential barrier of charge carriers; Originating from the Arrhenius thermal activation mechanism, this reflects the promoting effect of temperature on the carrier transition probability. The two are coupled in a product form, jointly determining the nonlinear growth behavior of conductivity under the combined effect of electric field and temperature.

[0055] This conductivity model offers significant advantages in physical accuracy. Firstly, its exponential function form sensitively captures the rapid increase in conductivity in defect regions caused by electric field distortion and localized overheating—conductivity can increase by orders of magnitude with even a small increase in electric field or temperature, which closely matches the nonlinear conductive behavior of insulating materials near breakdown. Secondly, the bivariate model simultaneously reflects the synergistic amplification effect of enhanced electric field and increased temperature on conductivity, avoiding the shortcomings of univariate models in underestimating the conductivity growth rate under strong electric field and high-temperature coupling scenarios. Compared to linear or power function models, this model more realistically reproduces the nonlinear dynamic characteristics of the entire process from slow degradation to accelerated thermal runaway of defects.

[0056] By independently calculating the target conductivity grid by grid, this method can accurately reconstruct the non-uniform degradation process caused by uneven electric field and temperature distribution in the defect region, revealing the physical law that degradation always starts from the most severe weak point inside and spreads outward.

[0057] Step S32: Determine the absolute value of the ratio of the difference between the target conductivity and the preset conductivity of each grid cell in the current iteration to the preset conductivity; select the largest absolute value of the ratio from the absolute values ​​of the ratios of each grid cell as the relative rate of change of conductivity of the internal deterioration defect region in the current iteration.

[0058] The formula for calculating the relative rate of change of conductivity is:

[0059] in, This refers to the set of mesh cells within the internal degradation defect region. For the corresponding grid cell i In the current iteration k The relative rate of change of conductivity under the following conditions For the corresponding grid cell i In the current iteration k The conductivity value below, For the corresponding grid cell i In the current iteration k The target conductivity value is set below.

[0060] In this step, the reason for selecting the absolute value of the largest ratio from all grid cells as the representative rate of change for the region is that this maximum value corresponds to the most drastic and dangerous location within the defect region. Using the change amplitude at this most dangerous location as the decision basis for the overall time step can effectively ensure the stability of numerical calculations under the worst conditions.

[0061] Step S33: Compare the relative rate of change of conductivity with the preset upper limit threshold and lower limit threshold of the rate of change, and determine the time step of the next iteration based on the comparison result.

[0062] Specific regulatory strategies include the following three situations: When the relative rate of change of conductivity exceeds a preset upper limit threshold, the time step of the current iteration is adjusted. Multiply by reduction factor As the time step for the next iteration ;in, , To reduce the lower limit of the factor, To preset the upper limit of the rate of change of conductivity, For the current iteration k The relative rate of change of conductivity; When the relative rate of change of conductivity is less than a preset lower limit threshold, the time step of the current iteration is adjusted. Multiply by the recovery factor As the time step for the next iteration ;in, , This is the upper limit of the recovery factor. The lower limit of the preset rate of change of conductivity; When the relative rate of change of conductivity is between the preset upper limit threshold and the preset lower limit threshold: the time step of the current iteration is used as the time step of the next iteration.

[0063] Specifically, in this embodiment, the preset parameter values ​​are: = 0.5, = 0.1, = 0.25, = 1.2. This adaptive time step control mechanism achieves a balance between simulation accuracy and computational efficiency: it automatically reduces the step size when the conductivity changes drastically to ensure accuracy and stability, and appropriately restores the step size when the change is gradual to improve computational speed.

[0064] Step S34: Pass the corrected conductivity and the time step of the next iteration to the finite element composite model.

[0065] In the co-simulation architecture, this step is specifically implemented as follows: The third-party computing software, through a communication interface, sets the accurate target conductivity values ​​of each mesh element calculated in step S31 as the material properties of the corresponding mesh in the finite element model, and sets the time step determined in step S33 as the physical time span for the next transient solution. The corrected conductivity accurately reflects the conductivity level that should be achieved under the current electric field strength and temperature. The finite element software performs subsequent solutions based on this accurate value, ensuring physical correctness.

[0066] Step S4: Based on the corrected material parameters and the real-time distribution of electric field strength and temperature, the finite element composite model is solved again to update the distribution of electric field strength and temperature inside the cable joint in real time.

[0067] In the co-simulation architecture, after the third-party numerical calculation software completes the conductivity correction and time step adjustment, it transmits the corrected parameters to the finite element software via a communication interface. Specifically, the third-party calculation software uses parameter setting commands to set the corrected conductivity values ​​of each mesh element into the material properties of the corresponding mesh in the finite element model, and sets the physical time span of the transient solution according to the adjusted time step; then, it uses a model update command to update the finite element model to apply the new parameter settings. After receiving the updated model parameters, the finite element software uses the corrected conductivity as the material parameter and performs a transient solution from the current time step at the specified time step. After the solution is completed, the finite element software returns the electric field intensity distribution and temperature distribution of each mesh element at the next time step to the third-party calculation software via the interface for use in the next round of correction. Since the corrected conductivity is the target value calculated based on the accurate field quantity at the current time, it is physically correct, and therefore the finite element solution results can truly reflect the electric field and temperature response after the evolution of the material parameters.

[0068] Step S5: Iteratively execute the real-time correction and re-solution steps to obtain the temperature distribution at each iteration time until the iteration termination condition is determined.

[0069] By repeatedly executing steps S3 and S4, the third-party calculation software and the finite element software collaboratively complete the entire joint simulation calculation, obtaining the time-domain sequence of temperature distribution in the defect region under each iteration, and thus obtaining the temperature field distribution of the entire dynamic process of the deterioration defect region inside the cable joint. The specific flowchart of the simulation method for the dynamic development process of the deterioration defect region inside the cable joint in this embodiment can be found in [reference needed]. Figure 2 .

[0070] After each iteration of the finite element method (FEM) software, third-party calculation software can determine whether the iteration termination condition is met based on the temperature distribution data returned by the FEM software. The iteration termination condition in this method includes two scenarios: first, determining that the maximum temperature of each mesh element within the internal degradation defect region exceeds a preset temperature threshold; and second, determining that the internal degradation defect region has reached thermal equilibrium.

[0071] The preset temperature threshold is an empirically determined value based on the thermal properties of the insulating material. In one embodiment, taking polyethylene insulation as an example, the preset temperature threshold can be set to 350°C to 380°C. This value is close to the melting point of polyethylene, and reaching this temperature means that the insulating material is at direct risk of thermal breakdown. After obtaining a new temperature distribution each time, third-party calculation software checks whether the maximum temperature of the internal deterioration defect area exceeds the preset temperature threshold. If it does not exceed the threshold, the next iteration continues; if it does exceed the threshold, the iteration termination condition is determined, and the iteration process terminates.

[0072] The thermal equilibrium of the internal degradation defect region can be determined as follows: During the iteration process, if the temperature of the internal degradation defect region does not exceed a preset temperature threshold, third-party computing software synchronously monitors its temperature change rate. When the average temperature change rate of each grid cell in the internal degradation defect region is lower than the preset thermal equilibrium convergence threshold over n consecutive iterations (n ​​is preferably an integer greater than or equal to 3), it indicates that the system's heat generation and dissipation have reached a dynamic balance, and the temperature no longer changes significantly. At this point, thermal equilibrium is determined to have been reached, and the iteration is terminated. This branch corresponds to the scenario where the defect development eventually stabilizes and thermal breakdown does not occur. The steady-state temperature recorded at this time can be used to assess whether the defect poses a long-term operational risk.

[0073] Furthermore, once it is determined that the maximum temperature of each grid cell within the internal degradation defect region exceeds a preset temperature threshold, the mere fact that the temperature exceeds the threshold is insufficient to accurately pinpoint the onset of thermal runaway. The critical temperature for thermal breakdown can be automatically identified from the simulation data by analyzing the second derivative behavior of the temperature-time curve.

[0074] Specifically, third-party computing software can be used to calculate the second derivative of temperature with respect to time for each grid cell within the internal degradation defect region, corresponding to the maximum temperature of that grid cell in each iteration. The second derivative reflects the acceleration of the temperature rise rate and is a key indicator for identifying the thermal runaway inflection point (i.e., the critical thermal breakdown inflection point). Before the inflection point, although the temperature rise rate increases slowly, the second derivative value is very small; at the inflection point, the exponential growth effect of the conductivity-temperature positive feedback begins to appear, and the temperature rise rate suddenly changes from "slowly increasing" to "rapidly increasing," with a significant jump in the second derivative between adjacent iterations; after the inflection point, the second derivative remains relatively large. Therefore, by monitoring the ratio of the second derivative values ​​between adjacent iterations, the moment of this jump can be located.

[0075] More specifically, starting from the first iteration, the ratio of the second derivative of each iteration to the second derivative of the previous iteration can be calculated progressively. For the grid cell corresponding to the maximum temperature, when for the first time in m consecutive iterations, the ratio of the second derivative values ​​in each iteration exceeds a preset ratio threshold, the system is determined to have stably entered an irreversible thermal runaway state. At this point, the temperature corresponding to the first iteration in these m consecutive iterations (m is preferably an integer greater than or equal to 3) is determined as the thermal breakdown critical temperature.

[0076] It should be noted that in this embodiment, analyzing the second derivative behavior of the maximum temperature in the defect region with respect to time is a preferred simplified algorithm, which can reduce the amount of computation and improve computational efficiency. In other embodiments, other methods can also be used to identify thermal runaway (i.e., the critical thermal breakdown inflection point), for example, taking the average temperature and the average value of the second derivative of each grid cell, and then determining whether it exceeds a preset temperature threshold to determine whether thermal runaway has occurred.

[0077] It should be noted that the thermal breakdown critical temperature is conceptually different from the preset temperature threshold used to terminate the iteration: the preset temperature threshold is an engineering judgment threshold used to trigger the termination of the iteration, usually set near the melting point or even the ignition point of the insulating material. The thermal breakdown critical temperature, on the other hand, is a characteristic temperature reflecting the physical starting point of thermal runaway, obtained through a detailed analysis of the second derivative behavior of the temperature curve. It can provide a quantitative basis for cable condition assessment and fault early warning.

[0078] Figure 5 The results of thermal field calculations for the critical thermal breakdown moment obtained using the method of the present invention are shown. As can be seen from the figure, the temperature rise at the location of the insulation defect is significant, reaching the melting point or even the ignition point of polyethylene.

[0079] As can be seen, the co-simulation method described in this paper can effectively obtain the temperature distribution and thermal breakdown temperature during the entire dynamic process of internal degradation defects in cable joints, thus achieving simulation of the breakdown process. Traditional simulation methods, which set material parameters to constant values, cannot reflect the nonlinear evolution of conductivity under electrothermal coupling, and therefore cannot simulate insulation breakdown considering defects. This method overcomes the shortcomings of traditional simulation methods, such as insufficient consideration of dynamic characteristics and the inability of traditional methods to accurately describe the development and evolution of defects under dynamic operating conditions.

[0080] According to a second aspect of the present invention, a device for simulating the dynamic development process of internal degradation defects in cable joints is provided, the device utilizing the method described in the first aspect of the present invention. Specifically, the device includes: The modeling module is used to create a finite element composite model of the internal electrothermal field of the cable joint, including the internal deterioration and defect area. The solution module is used to solve the finite element composite model based on preset working conditions to obtain the real-time distribution of electric field intensity and temperature inside the cable joint. The correction module is used to correct the material parameters at the internal deterioration defect area in real time based on the real-time distribution of electric field strength and temperature. The update module is used to update the distribution of electric field strength and temperature inside the cable joint in real time based on the material parameters that are corrected in real time.

[0081] Furthermore, the device also includes: The prediction module is used to determine whether thermal shock will occur inside the cable joint and predict the time of thermal breakdown based on the real-time temperature distribution inside the cable joint.

[0082] According to a third aspect of the present invention, a terminal is provided, comprising a processor and a storage medium. The storage medium is used to store instructions, and the processor is used to execute the steps of the above-described simulation method according to the instructions.

[0083] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0084] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0085] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0086] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A simulation method for the dynamic development process of internal deterioration defects in cable joints, characterized in that, Includes the following steps: A finite element composite model of the internal electrothermal field of the cable joint, including the internal deterioration defect region, was established. The finite element composite model is solved based on the preset initial working conditions to obtain the real-time distribution of electric field intensity and temperature inside the cable joint. Based on the current distribution of electric field intensity and temperature, the conductivity at the internal deterioration defect region is corrected in real time. Based on the corrected conductivity and the current distribution of electric field intensity and temperature, the finite element composite model is re-solved to update the distribution of electric field intensity and temperature at the next moment. The process involves iteratively performing real-time corrections and resolving the problem to obtain the temperature distribution at each iteration time, until the iteration termination condition is determined.

2. The simulation method for the dynamic development process of internal deterioration defects in cable joints according to claim 1, characterized in that, The real-time correction of conductivity at internal deterioration defect areas includes: Traverse each grid cell within the internal degradation defect region, obtain the electric field intensity and temperature of the corresponding grid cell at the current moment, and calculate the target conductivity of each grid cell for the current iteration based on the preset conductivity model, as the corrected conductivity.

3. The simulation method for the dynamic development process of internal deterioration defects in cable joints according to claim 2, characterized in that, The preset conductivity model is as follows: in, For the corresponding grid cell i In the current iteration k The target conductivity is as follows. For the corresponding grid cell i In the current iteration k electric field strength under, For the corresponding grid cell i In the current iteration k temperature, A , B , C These are the first, second, and third empirical coefficients, respectively.

4. The simulation method for the dynamic development process of internal deterioration defects in cable joints according to claim 2, characterized in that, The real-time correction of conductivity at internal deterioration defect areas also includes: Determine the absolute value of the ratio of the difference between the target conductivity and the preset conductivity of each grid cell in the current iteration to the preset conductivity; The largest absolute value of the ratio is selected from the absolute values ​​of the ratios of each grid cell and used as the relative rate of change of conductivity of the internal deterioration defect region in the current iteration. The relative rate of change of conductivity is compared with preset upper and lower thresholds of the rate of change, and the time step of the next iteration is determined based on the comparison results. The corrected conductivity and the time step for the next iteration are passed to the finite element composite model.

5. The simulation method for the dynamic development process of internal deterioration defects in cable joints according to claim 4, characterized in that, The relative rate of change of conductivity is compared with preset upper and lower thresholds for the rate of change, and the time step for the next iteration is determined based on the comparison result, including: When the relative rate of change of conductivity exceeds a preset upper limit threshold, the time step of the current iteration is adjusted. Multiply by reduction factor As the time step for the next iteration ;in, , To reduce the lower limit of the factor, To preset the upper limit of the rate of change of conductivity, For the current iteration k The relative rate of change of conductivity; When the relative rate of change of conductivity is less than a preset lower limit threshold, the time step of the current iteration is adjusted. Multiply by the recovery factor As the time step for the next iteration ;in, , This is the upper limit of the recovery factor. The lower limit of the preset rate of change of conductivity; When the relative rate of change of conductivity is between the preset upper limit threshold and the preset lower limit threshold: the time step of the current iteration is used as the time step of the next iteration.

6. The simulation method for the dynamic development process of internal deterioration defects in cable joints according to claim 4, characterized in that, The relative rate of change of conductivity of the corresponding grid in the current iteration is calculated as follows: in, This refers to the set of mesh cells within the internal degradation defect region. For the corresponding grid cell i In the current iteration k The relative rate of change of conductivity under the following conditions For the corresponding grid cell i In the current iteration k The conductivity value below, For the corresponding grid cell i In the current iteration k The target conductivity value is set below.

7. The simulation method for the dynamic development process of internal deterioration defects in cable joints according to claim 1, characterized in that, Determining that the iteration termination condition has been met includes: It is determined that the maximum temperature of each grid cell within the internal degradation defect region exceeds a preset temperature threshold; or The internal deterioration defect area was determined to have reached thermal equilibrium.

8. The simulation method for the dynamic development process of internal deterioration defects in cable joints according to claim 7, characterized in that, The method further includes: After determining that the maximum temperature of each grid cell in the internal deterioration defect region exceeds a preset temperature threshold, the grid cell corresponding to the maximum temperature is determined, and the second derivative of temperature with respect to time for that grid cell is calculated in each iteration. In each iteration of the grid cell, when the ratio of the second derivative value of each iteration to the value of the previous iteration exceeds a preset ratio threshold in the first consecutive m iterations, the temperature corresponding to the first iteration in the first consecutive m iterations is determined as the thermal breakdown critical temperature; where m is an integer greater than or equal to 3.

9. A simulation device for the dynamic development process of internal deterioration defects in cable joints using the method described in any one of claims 1-8, characterized in that, include: The modeling module is used to create a finite element composite model of the internal electrothermal field of the cable joint, including the internal deterioration and defect area. The initial solution module is used to solve the finite element composite model based on preset initial working conditions to obtain the real-time distribution of electric field intensity and temperature inside the cable joint. The correction module is used to correct the material parameters at the internal deterioration defect area in real time based on the current electric field strength and temperature distribution. The update module is used to re-solve the finite element composite model based on the corrected material parameters and the current electric field intensity and temperature distribution, so as to update the electric field intensity and temperature distribution at the next moment. The iteration module is used to iteratively perform real-time correction and re-solution steps. Based on the temperature distribution under each iteration, the iteration is terminated once thermal runaway is determined or thermal equilibrium is reached.

10. A terminal, comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1-8.

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