A low-voltage line insulation damage early fault modeling method

Abstract

The application discloses a kind of low-voltage line insulation damage early fault modeling methods, it is related to low-voltage line fault simulation technical field, comprising: S1, selection solving space dimension, physical field interface and research solver;S2, establish geometric model, set material physical property parameter, boundary condition and initial condition, divide grid;S3, set solving time and output step;S4, solution calculation and judge whether the solution result is reasonable, if unreasonable then return S2, if reasonable then enter S5;S5, analysis is carried out to simulation calculation result.The application can realize the accurate positioning and intelligent diagnosis of equipment early fault, improve the reliability and stability of distribution network.

Description

Technical Field

[0001] This invention relates to the field of low-voltage line fault simulation technology, and more specifically to a method for modeling early-stage faults caused by insulation damage in low-voltage lines. Background Technology

[0002] As a crucial hub in the "last mile" of the power system, power distribution equipment undertakes the core functions of power distribution, voltage regulation, and secure transmission. Its operating status directly affects the electricity experience of end users and the stability of socio-economic activities. Against the backdrop of large-scale power development and utilization, the integration of a high proportion of renewable energy sources has led to rapid changes in the distribution network topology. To address the challenges of this new situation, a full-cycle prevention and control system of "early warning and proactive intervention" has become an important measure to improve power supply reliability and a significant breakthrough in expanding fault defense systems and achieving proactive early warning.

[0003] Low-voltage lines are a crucial component of urban power distribution networks, undertaking the core task of power transmission. However, my country's low-voltage lines have long faced the problem of insufficient maintenance resources. With increasing service life, they are continuously subjected to mechanical stress, erosion from humid environments, and natural aging, making the insulation layer highly susceptible to damage. This can lead to early fault arcing, which, after repeated discharges, develops into a permanent fault. Compared to other types of faults, insulation failure faults are characterized by high current and high heat generation, posing significant safety hazards.

[0004] For low-voltage lines, traditional periodic inspection methods such as infrared thermal imaging, partial discharge detection, and drone patrols can effectively detect potential faults, but they are costly to maintain and difficult to achieve full-time, all-area coverage. Moreover, low-voltage lines involve a large number of diverse and complex devices, and the environments, causes, and mechanisms of early-stage faults vary greatly among different devices, resulting in voltage and current signals with different characteristics.

[0005] Therefore, how to study the early fault arc of insulation damage types in cable faults, achieve accurate location and intelligent diagnosis of early equipment faults, and improve the reliability and stability of the power distribution network is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a method for modeling early faults in low-voltage line insulation damage, which solves the problems existing in the background technology.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for modeling early-stage faults caused by insulation failure in low-voltage lines includes the following steps:

[0009] S1. Select the solution space dimension, physics interface, and study the solver;

[0010] S2. Establish the geometric model, set the material properties, boundary conditions and initial conditions, and generate the mesh;

[0011] S3, Set the solution time and output step size;

[0012] S4. Solve the calculation and determine whether the solution is reasonable. If it is not reasonable, return to S2. If it is reasonable, proceed to S5.

[0013] S5. Analyze the simulation results.

[0014] Optionally, S1 is as follows:

[0015] Considering the early fault arc of a low-voltage cable with insulation damage as the research object, the arc evolution process of the cable insulation damage fault arc is similar in different cross sections, so two-dimensional simulation modeling is adopted;

[0016] The system sets up temperature field, flow field, electric field, and magnetic field. The coupling of temperature field and flow field is achieved through a non-isothermal flow module. The coupling of temperature field and electric field is achieved through a balanced discharge heat source module and an electromagnetic heat module. The coupling of magnetic field and flow field is achieved through a magnetohydrodynamic module.

[0017] Arc simulation based on magnetohydrodynamics focuses on the macroscopic evolution and development of the arc over a certain time scale. Therefore, a transient approach is chosen for the solution, and a separate solution strategy is adopted.

[0018] Optionally, temperature field, flow field, electric field, and magnetic field can be set, specifically as follows:

[0019] A current field calculation model is constructed using a current module to solve the spatial distribution characteristics of current density in the arc region. Based on Maxwell's equations, the conduction path of current in cable conductors, insulation defect gaps, and air is quantitatively characterized by coupling the conductivity parameters of the arc plasma with the electromagnetic field control equations.

[0020] The magnetic field module is used to perform fine modeling and numerical calculation of the magnetic field of the electric arc and its surrounding space, so as to obtain the spatial distribution characteristics and vector direction of the magnetic field strength.

[0021] The laminar flow module is used to simulate and describe the laminar flow of electric arc plasma, and to obtain the plasma velocity, direction and velocity distribution.

[0022] The heat transfer process between the electric arc plasma and the surrounding environment is calculated using a fluid heat transfer module, which yields the temperature distribution of the electric arc and the propagation of heat in space.

[0023] Optionally, in S2, a geometric model is established, specifically as follows:

[0024] To prepare faulty cables with insulation damage, a basic shape is created using parametric geometry tools.

[0025] Based on the relative relationship between the location of the damage and the cable body, the insulation damage types are divided into damage to the central insulation layer and damage to the side insulation layer.

[0026] By integrating the insulating material areas of the geometric structure and treating them as a unified physical region, ignoring the outer insulating tape, and setting up separate regions in the main arc-generating areas, a simplified geometric structure of the cable with insulation damage is obtained.

[0027] Optionally, in S2, the material properties include specific heat capacity, electrical conductivity, density, and thermal conductivity; among them, the properties of copper and polyvinyl chloride are set as fixed constants, and the properties of air are derived from the gas discharge plasma basic database.

[0028] Optionally, in S2, the boundary conditions and initial conditions are set as follows:

[0029] The air boundary is an open boundary, the air pressure is set to one standard atmosphere, the ambient temperature is set to 293.15K, the boundary is set to a no-slip boundary, and the initial values ​​of pressure and velocity in the laminar flow region are both set to 0.

[0030] A stable electric arc exists at the start of the simulation, and an initial electric arc region is set in the air between the cable conductors;

[0031] The initial phase of the power frequency AC voltage source is set to -90° to ensure that the voltage value output by the voltage source at the moment of simulation start is at its peak, thereby matching the conductivity characteristics of the existing stable arc plasma.

[0032] Optionally, in S2, the network is divided as follows:

[0033] The free triangular meshing method was adopted, and the maximum cell size was set to 0.36, and the resolution of narrow areas was set to 1.0.

[0034] The narrow area is divided into finer grids, with the maximum cell size set to 0.104 and the resolution of the narrow area set to 1.0.

[0035] Optionally, in S3, the solution time is set to 0-100ms, and the output step size is set to 0.1ms.

[0036] Optional, S5 specifically includes:

[0037] The Joule heat generated during arc combustion creates a non-uniform temperature field in space. The temperature at the edge of the arc is lower than that at the center due to heat transfer from the fluid. The arc temperature reacts to the arc development. The high conductivity of the medium in the high-temperature center region forms a local low-impedance channel, driving the current to concentrate in the center region. This thermo-electric bidirectional coupling process makes the fault arc current density and temperature field exhibit a dynamic coupling relationship.

[0038] In the simulation model of central insulation layer failure, the electric arc mainly occurs in the central region of the two cables, and the temperature field exhibits an axisymmetric distribution characteristic.

[0039] In the simulation model of side insulation layer damage, the electric arc occurs in the side insulation damage area, and the temperature field shows a fan-shaped distribution.

[0040] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for modeling early faults in low-voltage line insulation damage, which has the following beneficial effects:

[0041] This invention takes magnetohydrodynamics theory as its core and constructs a multi-physics coupled model of low-voltage line insulation failure arc based on the COMSOL simulation platform. By scientifically setting the model's physical property parameters, initial conditions, boundary conditions, and physical field control equations, it ensures that the model can realistically reproduce the dynamic process of the fault arc. On this basis, the simulation results of the obtained arc temperature field morphology, current density distribution, and fault signal waveform are analyzed, providing a theoretical basis for the identification of insulation failure faults and playing an important role in ensuring the safe and stable operation of the distribution network. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0043] Figure 1 A flowchart of the early fault modeling method for low-voltage line insulation damage provided by the present invention;

[0044] Figure 2 A schematic diagram showing the details of the multiphysics field setup provided by this invention;

[0045] Figure 3 External circuit diagram of the simulation model provided for this invention;

[0046] Figure 4 The diagram shows the arc current density distribution and temperature distribution provided by the present invention; (a) shows the type of central insulation failure at 13.6 ms, and (b) shows the type of side insulation failure at 7.3 ms.

[0047] Figure 5 The maximum arc temperature curve provided for this invention; (a) represents the center insulation failure fault, and (b) represents the side insulation failure fault;

[0048] Figure 6 This invention provides a side insulation failure fault signal.

[0049] Figure 7 This invention provides a center insulation failure fault signal. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] This invention discloses a method for modeling early-stage faults in low-voltage line insulation damage, such as... Figure 1 As shown, it includes the following steps:

[0052] S1. Select the solution space dimension, physics interface, and study the solver;

[0053] S2. Establish the geometric model, set the material properties, boundary conditions and initial conditions, and generate the mesh;

[0054] S3, Set the solution time and output step size;

[0055] S4. Solve the calculation and determine whether the solution is reasonable. If it is not reasonable, return to S2. If it is reasonable, proceed to S5.

[0056] S5. Analyze the simulation results.

[0057] In this embodiment, the multiphysics simulation analysis software COMSOL is used to simulate the electric arc. COMSOL is widely used in modeling and simulating complex physical phenomena in engineering, physics, chemistry, biology, and other fields. COMSOL's core advantage lies in its ability to couple and analyze multiple physical fields such as electromagnetics, heat, structural mechanics, fluid dynamics, and acoustics. It can accurately simulate the interaction mechanisms of multiple physical processes under real-world conditions, helping researchers reveal the essence of physical phenomena, optimize system design, and simulate system evolution trends. Next, referring to... Figure 1 It details the entire process from model building, parameter setting, mesh generation to solution analysis, providing clear guidance for the standardization and repeatability of simulation work.

[0058] I. Selecting the solution space dimension, physics interface, and studying the solver

[0059] 1) COMSOL offers one-dimensional, two-dimensional, and three-dimensional spatial dimensions. This embodiment studies the early fault arc of a low-voltage cable with insulation damage, requiring modeling of the cable cross-section and surrounding empty area. Therefore, two-dimensional or three-dimensional modeling is necessary. Three-dimensional simulation can fully present the cable and arc in real space, comprehensively and accurately reflecting the physical process, but it involves extremely high computational load, demanding hardware, and is time-consuming, with complex model construction and setup. Two-dimensional simulation considers the cable cross-section and can analyze physical phenomena in the cross-section and a selected axial plane, such as electric and magnetic field distribution and heat conduction. It strikes a balance between computational efficiency and accuracy, facilitates visualization of results, and better addresses the analysis needs of the arc's physical process while considering computational resources and efficiency. It can effectively study the interaction between the arc and the cable in the cross-section and selected axial plane. Since the arc evolution process of a cable insulation damage fault arc is similar across different cross-sections, two-dimensional simulation can more comprehensively reflect its dynamic evolution process. Therefore, this embodiment ultimately chooses to use two-dimensional simulation modeling.

[0060] 2) The evolution of the macroscopic state of the electric arc over time and space can be calculated through the coupling of temperature field, flow field, electric field, and magnetic field. Therefore, the core of the simulation lies in setting up and coupling these four physical fields. COMSOL provides various physical fields required for simulation. The fluid heat transfer module is used to set up the temperature field; the laminar flow module is used to set up the gas flow field; the current module and circuit module are used to construct the electric field and external circuits; and the magnetic field module is used to set up the magnetic field. In the multiphysics module, the coupling of temperature field and flow field is achieved through the non-isothermal flow module; the coupling of temperature field and electric field is achieved through the equilibrium discharge heat source module and the electromagnetic heat module; and the coupling of magnetic field and flow field is achieved through the magnetohydrodynamics module.

[0061] A. Single Physics Field Setup

[0062] This embodiment incorporates a current module into the simulation model to construct a current field calculation model, focusing on solving the spatial distribution characteristics of current density in the arc region. Based on Maxwell's equations, the conduction path of current in the cable conductor, insulation defect gaps, and air is quantitatively characterized by coupling the conductivity parameters of the arc plasma with the electromagnetic field control equations. The simulation model strictly defines the boundaries of the computational domain, defining the range of the current field as the cable metal layer, PVC insulation layer, and air domain, thereby accurately reflecting the non-uniform characteristics of current density distribution under insulation failure scenarios. The calculation results provide physical constraints for subsequent arc heat source loading and temperature field iterative calculations.

[0063] This embodiment introduces a high-precision magnetic field module into the simulation model to perform refined modeling and numerical calculation of the magnetic field in the electric arc and its surrounding space, accurately obtaining the spatial distribution characteristics and vector direction of the magnetic field intensity. By solving for the magnetic field distribution, input parameters are provided for the electromagnetic-thermal and magnetohydrodynamic modules, thereby realizing the constraint and effect of the magnetic field on the electric arc plasma in three different media.

[0064] This embodiment accurately simulates and describes the laminar flow of electric arc plasma by incorporating a laminar flow module into the simulation model. In an electric arc environment, the plasma flow state significantly influences the characteristics and behavior of the arc. The laminar flow module allows for the accurate calculation of parameters such as plasma velocity, direction, and velocity distribution, providing a foundation for in-depth research into the arc's transmission process and energy distribution. Based on material properties, the effective range of the laminar flow field is set to air, and the temperature output from the non-isothermal flow field and the pressure output from the laminar flow field are used as input parameters for the model.

[0065] This embodiment accurately calculates the heat transfer process between the electric arc plasma and its surrounding environment by incorporating a fluid heat transfer module into the simulation model. It considers multiple heat transfer mechanisms, including conduction, convection, and radiation. By calculating these heat transfer processes, the temperature distribution of the electric arc and the propagation of heat in space can be obtained, which helps in analyzing the heating effect of the electric arc on the surrounding medium and its own cooling mechanism. Based on material properties, the effective range of the fluid heat transfer field is set to air, cables, and insulation layers. Air is treated as a fluid, while cables and insulation layers are treated as solids. The temperature output from the temperature field and the absolute pressure output from the non-isothermal flow field are used as input parameters for the model.

[0066] B. Multiphysics Setup

[0067] Given that arc development is essentially a complex coupled system involving the interaction of multiple physical processes, this embodiment constructs a simulation system based on practical research needs, comprising four core modules: non-isothermal flow, equilibrium discharge heat source, electromagnetic thermal effect, and magnetohydrodynamics. Through the synergistic effect and data interaction between multiple modules, precise control of the coupled processes of multiple physical fields such as flow field, electric field, magnetic field, and temperature field in plasma arc is achieved, thereby more realistically reproducing the physical mechanism of arc dynamic development.

[0068] Because an electric arc is a high-temperature plasma, its internal temperature distribution is extremely uneven. The temperature in the central region of the arc can reach thousands or even tens of thousands of Kelvin, while the temperature in the peripheral regions is relatively low. This temperature unevenness significantly affects various physical properties of the plasma arc, such as specific heat capacity, electrical conductivity, density, and thermal conductivity. Therefore, a non-isothermal flow module needs to be added to the arc simulation model to consider the changes in fluid parameters caused by temperature variations. Simultaneously, the arc's development is accompanied by complex heat convection and heat conduction. The non-isothermal flow module can simultaneously consider both heat transfer mechanisms, accurately simulating the heat transfer process in the arc by calculating the coupling effect of the temperature field and the flow field. In this embodiment, the non-isothermal flow module couples laminar flow and fluid heat transfer physical fields by inputting temperature and pressure parameters.

[0069] In actual electric arc discharge, the power source continuously inputs energy into the arc to maintain its existence and combustion. This embodiment uses two modules: a balanced discharge heat source and an electromagnetic heat source, coupled with current and fluid heat transfer interfaces to simulate this stable energy input process. This ensures that the energy state of the arc in the simulation matches the actual situation, thereby guaranteeing that the arc can exist and develop stably in the simulation environment. This helps to accurately simulate various characteristics of the arc, such as temperature distribution.

[0070] Arc plasma can be considered as a conductive fluid, and it experiences a Lorentz force in a magnetic field. This embodiment incorporates a magnetohydrodynamic module to calculate the Lorentz force and electromotive force, coupling the laminar flow field and magnetic field to simulate electromagnetically driven fluid flow. Details of the relevant physics field settings are as follows... Figure 2 As shown.

[0071] 3) COMSOL offers three solution modes: frequency domain, steady-state, and transient. The transient solution mode can accurately capture the dynamic changes of the physical field over time, making it suitable for analyzing transient processes of evolution. However, it requires setting parameters such as the time step, resulting in high computational load, long processing time, and high hardware performance requirements. Arc simulation based on magnetohydrodynamics mainly focuses on the macroscopic evolution of the arc over a certain time scale; therefore, the transient mode is chosen for solution. A separate solution strategy is adopted. Multi-physics coupled problems are usually complex, involving the interaction of multiple physical processes. The separate solution mode decomposes these complex physical processes and solves each physical field separately. This method has significant advantages: firstly, it effectively reduces computational load, avoiding excessive consumption of computational resources due to simultaneously solving multiple highly coupled equations, thus improving computational efficiency; secondly, it facilitates the individual control and optimization of the solution process for each physical field.

[0072] II. Establish the geometric model, set material properties, boundary conditions and initial conditions, and generate the mesh.

[0073] 1) Geometric model

[0074] To prepare a cable with insulation damage, a basic shape is created using parametric geometry tools. Specifically, based on the national standard GB / T31143-2014, the cable with insulation damage is prepared as follows: Insulating tape is used to bond two cables with a cross-sectional area of ​​1.5 mm². 2 The wires are tightly bundled, and the cable test sample is cut into a minimum length of 200mm. The insulation layer is cut in the middle of the cable. The cutting depth should be deep enough to expose the wire core, but without damaging the metal conductor. Finally, the cut is wrapped with two layers of insulating tape.

[0075] Due to the influence of the actual operating environment, the degree of damage to the cable insulation layer varies. These factors all have an important impact on the development of the electric arc. Therefore, it is necessary to fully consider the actual working conditions and classify the insulation damage type into central insulation layer damage and side insulation layer damage based on the relative relationship between the damage location and the cable body.

[0076] The insulating material regions of the geometric structure are integrated and regarded as a unified physical region; the outer insulating tape undergoes rapid pyrolysis in the early stage of arc combustion, which has a weak impact on the dynamic development process of the arc, so it is ignored; a separate region is set in the main arc occurrence area, which is only used to divide a denser network to obtain the simplified geometric structure of the cable with insulation damage, ensuring model convergence.

[0077] 2) Physical property parameters

[0078] Material properties include specific heat capacity, electrical conductivity, density, and thermal conductivity. Electrical conductivity directly determines the ability of plasma to conduct current. According to Ohm's law, under a given electric field, higher conductivity results in greater current density and more Joule heat. Specific heat capacity determines the magnitude of temperature change when plasma absorbs or releases heat. Joule heat raises the plasma temperature, and specific heat capacity affects the establishment and change of the temperature field, thus influencing the state and properties of the plasma. Density affects the mechanical properties and thermophysical processes of plasma. In flow field analysis, density is a key parameter in computational fluid dynamics equations; it interacts with variables such as pressure and velocity to determine the flow characteristics of the plasma. Thermal conductivity describes the ability of plasma to conduct heat. High thermal conductivity means faster heat conduction within the plasma, contributing to a more uniform temperature field. In arc plasma, thermal conductivity determines the rate at which heat is transferred from high-temperature regions such as the arc center to low-temperature regions such as the electrodes. It is crucial for analyzing the thermal load on the electrodes, heat exchange between the plasma and the surrounding medium, and the stable distribution of the temperature field.

[0079] The simulation model in this embodiment involves three materials: air, copper, and polyvinyl chloride (PVC). In comparison, the changes in the physical properties of copper and PVC under the action of an electric arc have a smaller impact on the development of the arc. To balance computational accuracy and efficiency, the physical property parameters of copper and PVC are set as fixed constants in this simulation, while the physical property parameters of air are derived from the basic database of gas discharge plasma.

[0080] 3) Boundary conditions and initial conditions

[0081] When simulating arc faults caused by insulation failure, setting appropriate initial and boundary conditions is crucial to ensuring the realism and reliability of the simulation results. Initial conditions define the arc's triggering point and initial physical state, while boundary conditions influence the arc's development by constraining the system's energy exchange and physical field evolution. A multi-physics arc simulation model based on magnetohydrodynamics theory requires setting initial and boundary conditions for four physical fields—current, magnetic field, temperature field, and flow field—that conform to actual operating conditions.

[0082] Low-voltage power distribution lines often occur in open atmospheric environments. Therefore, the air boundary is an open boundary, the air pressure is set to one standard atmosphere, the ambient temperature is set to 293.15K, the boundary is set to a no-slip boundary, and the initial values ​​of pressure and velocity in the laminar flow region are both set to 0.

[0083] At the start of the simulation, a stable electric arc exists, and an initial arc region is set in the air between the cable conductors; since the arc has been burning stably, the temperature is usually several thousand Kelvin, and the initial temperature in this model is set to 5000K;

[0084] In the construction of the simulation model, voltage and current are determined by... Figure 3 The external circuit shown includes a 220V AC power frequency voltage source, a 50Ω current-limiting resistor R, and a fault arc model. The arc terminal is connected in series with the line resistor and then grounded. An ammeter and voltmeter are added to the circuit to detect voltage and current changes during the arc generation process. Since a stable arc plasma already exists at the start of the simulation, the initial phase of the AC power frequency voltage source is set to -90° to ensure that the voltage output is at its peak value at the moment the simulation starts. This matches the conductivity characteristics of the existing stable arc plasma and avoids abrupt changes in the arc state at the start of the simulation due to improper voltage phase.

[0085] 4) Mesh generation

[0086] When using COMSOL software to conduct magnetohydrodynamic multiphysics simulations of arc faults caused by insulation failure in low-voltage lines, finite element mesh generation is a crucial and interconnected step. It directly impacts the accuracy and efficiency of the simulation calculations and is a key foundation for ensuring the reliability of multiphysics coupling analysis. The implementation process must strictly adhere to scientific procedures and methods. Only through reasonable planning of mesh type, density distribution, and boundary conditions can accurate modeling and efficient solving of complex arc physical phenomena be achieved.

[0087] In this simulation, a free triangular mesh generation method was adopted. In terms of mesh generation parameters, the maximum cell size was set to 0.36 (limiting the maximum size of the mesh cells to ensure that the cells are not too large in the overall model, which would lead to the loss of key physical information), and the resolution of narrow regions was set to 1.0. For narrow regions, a finer mesh generation was performed, with the maximum cell size set to 0.104 and the resolution of narrow regions set to 1.0. This ensured that there was sufficient mesh resolution in these regions to accurately simulate the complex physical processes and avoid simulation distortion caused by sparse mesh.

[0088] The above meshing method offers high flexibility and can effectively adapt to the complex geometry of insulation failure sites in low-voltage lines. Regardless of whether the failure area is regular or irregular, the free triangular meshing method can effectively fill the gaps, ensuring accurate model discretization. Through the above parameter settings, the finite element meshing of the arc model for low-voltage line insulation failure faults is completed, laying a solid foundation for subsequent accurate multiphysics simulation calculations.

[0089] III. Setting the solution time and output step size

[0090] The development of a fault arc triggered by insulation failure is quite complex. The complete cycle from arc generation to extinction is the core of its dynamic evolution, and the continuous alternation of dozens of cycles throughout the combustion process demonstrates the complexity and regularity of the arc phenomenon. The entire process can last for a considerable time; therefore, setting the solution time to 0-100ms allows for detailed analysis of the periodic changes in the fault arc. Both the maximum simulation step size and the output step size are set to 0.1ms. A smaller maximum step size helps improve the accuracy of the simulation results and ensures the convergence of the simulation model. A smaller output step size can more meticulously depict the changes in the physical characteristics of the arc at various instants, such as the arc's temperature distribution, current density changes, and fault signal changes.

[0091] IV. Solve the problem and determine whether the solution is reasonable.

[0092] V. Simulation Result Analysis

[0093] 1) Evolution of fault arc

[0094] Taking the 13.6 ms of central insulation failure and the 7.3 ms of lateral insulation failure as examples, plot the arc current density and arc temperature distribution, as follows. Figure 4 As shown, the arc current density and temperature field exhibit a dynamic coupling relationship. This is because the Joule heat generated during arc combustion creates a non-uniform temperature field in space. The temperature in the center of the arc can reach over 6000K, while the temperature in the edge region is significantly lower due to fluid heat transfer. Simultaneously, the arc temperature influences arc development; the high conductivity of the medium in the high-temperature central region creates a localized low-impedance channel, driving the current to concentrate in the central region. Ultimately, this thermo-electrical bidirectional coupling process results in a highly nonlinear correlation between the arc current density distribution and the temperature field.

[0095] Overall, during the evolution of the arc temperature field, the arcs generated by center insulation failure faults and side insulation failure faults exhibit similar changing patterns, yet each displays its own unique temperature distribution characteristics and evolutionary properties due to differences in their respective conditions. Radially, the center of the arc column is the hottest region, with the arc temperature gradually decreasing outwards from the center. Axially, the arc root is the hottest region because it is in close contact with the electrode. Since the metal conductor itself is a solid, its heat transfer capacity is limited, resulting in relatively slow heat exchange between the arc root region and the surrounding environment.

[0096] Compared to center insulation failure faults, the shape of the gap in a side insulation failure fault significantly alters the discharge space of the arc. Because one side of the insulation layer remains intact, the fault arc can only develop on the damaged side and cannot freely propagate within the cable gap. This asymmetrical arc morphology results in a significant difference in the temperature field on both sides of the cable, creating an asymmetrical temperature distribution characteristic, in stark contrast to the relatively symmetrical temperature field in a center insulation failure fault. Simultaneously, due to the presence of an intact insulation layer on the other side, the arc in a side insulation failure fault exhibits a degree of distortion in the initial stage of arc initiation, resulting in a longer discharge path.

[0097] The minimum temperature of the gap in the side insulation failure type was 2906.6 K, higher than the 2594.6 K of the center insulation failure type. This difference stems from the significant impact of the cable insulation failure type on the intensity of gas thermal convection: side insulation failures are limited to a single-sided failure structure, and thermal convection can only occur on the damaged side, resulting in weaker thermal convection intensity compared to center insulation failures. Since thermal convection intensity directly affects the heat dissipation efficiency of the arc, weaker thermal convection causes the arc heat to dissipate slowly in side failures, thus maintaining a higher minimum temperature. Conversely, in center insulation failures, relatively sufficient thermal convection accelerates heat diffusion, resulting in a significantly faster temperature drop rate during the arc extinction phase compared to side insulation failures.

[0098] Figure 5The curve shows the maximum arc temperature changing over time, generally corresponding to the current and voltage waveforms. The rate of temperature change during the arc's ignition and extinguishing phases is particularly prominent. This is because the energy supply for maintaining combustion changes abruptly at the moment of arc state transition: during extinguishing, the energy input is rapidly interrupted, disrupting the original energy balance within the arc, and the high-temperature region cools rapidly due to the inability to continuously replenish energy; during ignition, the significant increase in energy input causes the arc temperature to rise rapidly. This drastic change in energy supply results in an extremely high rate of temperature change during the arc's state transition.

[0099] Under both insulation failure conditions, the peak arc temperature occurred earlier than the peak current waveform. This phenomenon indicates that the arc temperature exhibits a more rapid response characteristic during fault occurrence compared to current changes. This is because the arc continuously transfers heat to the surrounding air during combustion. As the current gradually increases, although the energy input to the arc increases, a large amount of energy also rapidly diffuses to the surrounding air through heat conduction, convection, and radiation. As the current approaches its peak value, the energy increment gained by the arc and the energy lost to the air reach a critical state, at which point the arc has limited energy to raise its own temperature. When the current approaches its peak value, the energy provided for arc combustion tends to stabilize, while the arc continues to transfer heat to the surrounding air. Furthermore, as the arc temperature increases, the energy transferred to the surrounding air continues to increase, resulting in a slight decrease in arc temperature when the current waveform reaches its peak due to continuous heat loss.

[0100] Simulation data shows that the arc peak occurs significantly earlier in center insulation failure faults than in side insulation failure faults. This phenomenon reveals that center failure, due to its larger fault area, results in higher heat transfer efficiency and more rapid heat diffusion. In the brief period before and after insulation breakdown, the temperature rises sharply; however, once the arc enters a stable combustion phase, the temperature begins to decrease thanks to relatively good heat dissipation. In stark contrast, in side insulation failure faults, due to impeded heat dissipation, the temperature maintains a synchronous upward trend during current rise, and the time interval between the temperature peak and the current peak is significantly shortened, demonstrating the significant impact of different failure locations on the thermal characteristics of the fault arc.

[0101] As can be seen from the above analysis, under the excitation of 220V AC voltage, the arc at the insulation failure point of the low-voltage line continues to evolve along the periodic trajectory of "arc ignition-burning-extinguishing-reignition". The arc extinguishes before each voltage crosses zero, and when the voltage rises in the reverse direction to the breakdown threshold, the arc will reignite at the failure point. This cycle repeats, showing the dynamic characteristics of AC fault arc.

[0102] 2) Fault arc waveform analysis

[0103] During the development of an electric arc, the voltage and current signals vary due to factors such as power supply characteristics, arc conductivity, surrounding medium, electrode material, and shape. The power supply voltage determines the basic power supply conditions for the arc; changes in arc properties alter conductivity, thus affecting voltage and current; the properties and pressure of the surrounding medium affect heat dissipation and ionization; and the electrode material and shape influence arc initiation and stability. Simultaneously, voltage provides energy to the arc to maintain the ionization state of the plasma, while the current magnitude determines the arc's energy input and temperature, thereby affecting its shape, brightness, and stability. Based on simulation results, arc voltage and current waveforms were plotted under two insulation failure conditions.

[0104] Breaking down air requires a certain voltage level. The voltage across the arc region during breakdown is related to the ease with which the arc reignites. The higher the breakdown voltage, the later the sudden increase in current occurs, and the longer the duration of the zero-wave plateau in the current waveform. Side-damage fault signals include... Figure 6 As shown, the peak fault current is 5.2A, the peak voltage is 272.32V, the average duration of a single arc is 5.5ms, and the zero-rest duration is stable at around 4.5ms. The fault signal for center insulation failure is as follows: Figure 7 As shown, the peak fault current is 5.4A, the peak voltage is 211.7V, the average duration of a single arc is 6.8ms, and the zero-rest duration is stable at around 3.2ms. Because the fault arc and temperature field distribution are coupled, the fault signal characteristics correspond to the temperature field distribution changes.

[0105] Considering the inherent periodicity of fault signals, and the fact that the fault arc requires 0.5 cycles to complete the dynamic process of "stable arcing-arc extinction-reignition-stable arcing," this embodiment takes the signal of an insulation failure fault in the 10ms-20ms range as an example to analyze the waveform characteristics of the fault arc and to explore in depth the evolution of the electrical signal during the arc's transition at different stages.

[0106] Overall, the current and voltage waveform trends of the fault arcs of the two insulation failure types are basically consistent. When the fault arc is in the "stable arcing" stage, the Joule heat generated by the arc is close to the heat dissipation through heat transfer, the arc conductivity is relatively stable, and the fault current is close to a standard sinusoidal waveform. When the fault arc enters the "arc extinction" stage, a large amount of heat is dissipated through heat transfer, the conductivity drops significantly, the fault current drops below 0.3A, and the fault voltage rises back to near the power supply voltage. When the fault arc is in the "arc re-ignition" stage, the conductivity rises significantly, the fault voltage drops rapidly, and the fault current rises rapidly. After a brief arc initiation process, the fault arc re-enters a stable arcing state, forming a periodic cycle of "stable arcing-arc extinction-re-arcing." During this process, the dynamic changes in the current and voltage waveforms clearly reflect the evolution of the electrical characteristics of the fault arc at different development stages.

[0107] Although the arc current and voltage waveforms of the two types of insulation failure exhibit similar overall evolution trends, significant differences remain in key characteristic parameters such as zero-rest duration, instantaneous current value, and signal amplitude. The reignition time of the arc in a side insulation failure fault lags significantly behind that of a center insulation failure fault arc, resulting in a zero-rest duration of 4.5 ms for the side insulation failure arc, significantly longer than the 3.2 ms for the center insulation failure arc. This is because the arc in a side insulation failure fault exhibits a certain degree of distortion, resulting in a longer arc length and a higher electric field strength required to break down the air, making reignition more difficult after the zero-crossing point.

[0108] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0109] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for modeling early-stage faults caused by insulation failure in low-voltage lines, characterized in that, Includes the following steps: S1. Select the solution space dimension, physics interface, and study the solver; S2. Establish the geometric model, set the material properties, boundary conditions and initial conditions, and generate the mesh; S3, Set the solution time and output step size; S4. Solve the calculation and determine whether the solution is reasonable. If it is not reasonable, return to S2. If it is reasonable, proceed to S5. S5. Analyze the simulation results; In S2, a geometric model is established, specifically as follows: To prepare faulty cables with insulation damage, a basic shape is created using parametric geometry tools. Based on the relative relationship between the location of the damage and the cable body, the insulation damage types are divided into damage to the central insulation layer and damage to the side insulation layer. By integrating the insulating material areas of the geometric structure and treating them as a unified physical area, ignoring the outer insulating tape, and setting up separate areas in the main arc occurrence areas, a simplified geometric structure of the cable with insulation damage is obtained. S5 specifically refers to: The Joule heat generated during arc combustion creates a non-uniform temperature field in space. The temperature at the edge of the arc is lower than that at the center due to heat transfer from the fluid. The arc temperature reacts to the arc development. The high conductivity of the medium in the high-temperature center region forms a local low-impedance channel, driving the current to concentrate in the center region. This thermo-electric bidirectional coupling process makes the fault arc current density and temperature field exhibit a dynamic coupling relationship. In the simulation model of central insulation layer failure, the electric arc mainly occurs in the central region of the two cables, and the temperature field exhibits an axisymmetric distribution characteristic. In the simulation model of side insulation layer damage, the electric arc occurs in the side insulation damage area, and the temperature field shows a fan-shaped distribution.

2. The method for modeling early-stage insulation damage in low-voltage lines according to claim 1, characterized in that, S1 specifically refers to: Considering the early fault arc of a low-voltage cable with insulation damage as the research object, the arc evolution process of the cable insulation damage fault arc is similar in different cross sections, so two-dimensional simulation modeling is adopted; The system sets up temperature field, flow field, electric field, and magnetic field. The coupling of temperature field and flow field is achieved through a non-isothermal flow module. The coupling of temperature field and electric field is achieved through a balanced discharge heat source module and an electromagnetic heat module. The coupling of magnetic field and flow field is achieved through a magnetohydrodynamic module. Arc simulation based on magnetohydrodynamics focuses on the macroscopic evolution and development of the arc over a certain time scale. Therefore, a transient approach is chosen for the solution, and a separate solution strategy is adopted.

3. The method for modeling early-stage insulation damage in low-voltage lines according to claim 2, characterized in that, The temperature field, flow field, electric field, and magnetic field are set up as follows: A current field calculation model is constructed using a current module to solve the spatial distribution characteristics of current density in the arc region. Based on Maxwell's equations, the conduction path of current in cable conductors, insulation defect gaps, and air is quantitatively characterized by coupling the conductivity parameters of the arc plasma with the electromagnetic field control equations. The magnetic field module is used to perform fine modeling and numerical calculation of the magnetic field of the electric arc and its surrounding space, so as to obtain the spatial distribution characteristics and vector direction of the magnetic field strength. The laminar flow module is used to simulate and describe the laminar flow of electric arc plasma, and to obtain the plasma velocity, direction and velocity distribution. The heat transfer process between the electric arc plasma and the surrounding environment is calculated using a fluid heat transfer module, which yields the temperature distribution of the electric arc and the propagation of heat in space.

4. The method for modeling early-stage insulation damage in low-voltage lines according to claim 1, characterized in that, In S2, the material properties include specific heat capacity, electrical conductivity, density, and thermal conductivity; among them, the properties of copper and polyvinyl chloride are set as fixed constants, while the properties of air are derived from the basic database of gas discharge plasma.

5. The method for modeling early-stage insulation damage in low-voltage lines according to claim 1, characterized in that, In S2, the boundary conditions and initial conditions are set as follows: The air boundary is an open boundary, the air pressure is set to one standard atmosphere, the ambient temperature is set to 293.15K, the boundary is set to a no-slip boundary, and the initial values ​​of pressure and velocity in the laminar flow region are both set to 0. A stable electric arc exists at the start of the simulation, and an initial electric arc region is set in the air between the cable conductors; The initial phase of the power frequency AC voltage source is set to -90° to ensure that the voltage value output by the voltage source at the moment of simulation start is at its peak, thereby matching the conductivity characteristics of the existing stable arc plasma.

6. The method for modeling early-stage insulation damage in low-voltage lines according to claim 1, characterized in that, In S2, the network is divided as follows: The free triangular meshing method was adopted, and the maximum cell size was set to 0.36, and the resolution of narrow areas was set to 1.

0. The narrow area is divided into finer grids, with the maximum cell size set to 0.104 and the resolution of the narrow area set to 1.

0.

7. The method for modeling early-stage insulation damage in low-voltage lines according to claim 1, characterized in that, In S3, the solution time is set to 0-100ms, and the output step size is set to 0.1ms.

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