Method for evaluating the electrical behavior of the inter-turn insulation of a superconducting magnet during short circuit arc propagation

Abstract

This application discloses a method for evaluating the conductivity behavior of the inter-turn insulation layer of a superconducting magnet during short-circuit arc propagation. The method includes: constructing a benchmark simulation structure with the same geometry as the experimental sample; configuring multiple different conductivity sub-models for the simulated insulating elements in the benchmark simulation structure corresponding to the inter-conductor insulation layer of the experimental sample, resulting in multiple experimental simulation models with different conductivity characteristics; applying a preset DC current consistent with the arc test to each of the multiple experimental simulation models, and determining multiple simulation results; performing a goodness-of-fit analysis between the multiple simulation results and the experimental results, and selecting the target simulation model with the highest goodness of fit to the experimental sample from the multiple experimental simulation models; evaluating the conductivity behavior of the inter-turn insulation layer based on the conductivity sub-model corresponding to the target simulation model. Thus, by comparing and fitting the experimental results with multiple simulation results, the influence of the arc on the conductivity behavior of the insulation layer can be analyzed, providing a basis for short-circuit arc risk assessment.

Description

Technical Field

[0001] This application relates to the field of electrical safety and arc behavior assessment technology for superconducting magnets, and in particular to a method for assessing the conductivity behavior of the inter-turn insulation layer of a superconducting magnet during the propagation of a short-circuit arc. Background Technology

[0002] During operation or quench failure, the inter-turn insulation layer of a superconducting magnet may break down, leading to a short-circuit arc. The arc's heat causes the insulation layer's conductivity to degrade from an insulating state to a conductive state. This degradation can affect the arc's combustion and propagation path, thus impacting the superconducting magnet's safe operation. However, current technologies struggle to directly obtain the conductivity characteristics of the inter-turn insulation layer under actual operating conditions. Therefore, the impact of this conductivity degradation on arc behavior remains unclear, resulting in a lack of basis for assessing the risk of arc failure in superconducting magnets. Summary of the Invention

[0003] This application provides a method for evaluating the conductivity behavior of the inter-turn insulation layer of a superconducting magnet during the propagation of a short-circuit arc.

[0004] This application provides a method for evaluating the conductivity behavior of an inter-turn insulation layer in a superconducting magnet during short-circuit arc propagation. The method includes: A benchmark simulation structure with the same geometry as the experimental sample is constructed. The experimental sample is matched with the superconducting magnet to be evaluated. The experimental sample is used for the arc test of the inter-turn insulation layer of the superconducting magnet. The benchmark simulation structure is provided with an arc channel at the simulated arc trigger position. The simulated arc trigger position corresponds to the preset arc trigger position of the experimental sample. The arc channel is used to simulate the initial arc. For the simulated insulating element in the benchmark simulation structure that corresponds to the conductor insulation layer of the experimental sample, multiple different conductivity sub-models are configured to obtain multiple experimental simulation models with different conductivity characteristics. Each experimental simulation model corresponds to one conductivity sub-model, and the conductivity sub-model is used to indicate the conductivity characteristics of the simulated insulating element in the experimental simulation model. A preset DC current consistent with the electric arc test is applied to multiple experimental simulation models respectively, and multiple simulation results are determined, wherein each simulation result corresponds to one of the experimental simulation models; The goodness-of-fit analysis is performed on multiple simulation results and experimental results, and the target simulation model with the highest goodness of fit with the experimental sample is selected from multiple experimental simulation models, wherein the experimental results are obtained based on the electric arc test; The conductivity behavior of the inter-turn insulation layer is evaluated based on the conductivity sub-model corresponding to the target simulation model.

[0005] Thus, a benchmark simulation structure with the same geometry as the experimental sample was constructed. The experimental sample was matched to the superconducting magnet and used for arc testing of the inter-turn insulation layer of the superconducting magnet. An arc channel was set at the simulated arc trigger position of the benchmark simulation structure, corresponding to the preset arc trigger position of the experimental sample. The arc channel was used to simulate the initial arc. Next, multiple different conductivity sub-models were configured for the simulated insulating element in the benchmark simulation structure corresponding to the inter-conductor insulation layer of the experimental sample, resulting in multiple experimental simulation models with different conductivity characteristics. Each experimental simulation model corresponds to a conductivity sub-model, which indicates the conductivity characteristics of the simulated insulating element in the experimental simulation model. Subsequently, a preset DC current consistent with the arc test was applied to each of the multiple experimental simulation models, and multiple simulation results were determined. Each simulation result corresponds to one experimental simulation model. Then, a goodness-of-fit analysis was performed on the multiple simulation results and experimental results. The target simulation model with the highest goodness of fit to the experimental sample was selected from the multiple experimental simulation models, where the experimental results were obtained based on the arc test. Finally, the conductivity behavior of the inter-turn insulation layer is evaluated based on the conductivity sub-model corresponding to the target simulation model. This ensures the reliability of the experimental results and the authenticity of the conductivity behavior assessment by constructing an experimental prototype that matches the actual superconducting magnet structure. Furthermore, by configuring an experimental simulation model with the same geometry as the experimental prototype and setting multiple conductivity levels, the simulation model can comprehensively cover different conductivity states of the inter-turn insulation layer. By comparing and fitting the experimental results of the prototype with the simulation results of multiple experimental simulation models, the equivalent conductivity characteristics of the inter-conductor insulation layer after insulation degradation can be determined. This allows for a quantitative analysis of the impact of electric arc on the conductivity behavior of the insulation layer, ultimately providing a reliable basis for the risk assessment of short-circuit arcs in superconducting magnets.

[0006] In some embodiments, the experimental specimen includes a first conductor, a second conductor, and an interconductor insulating layer arranged parallel to each other; Wherein, the cross-sectional dimensions of the first conductor are consistent with the cross-sectional dimensions of the conductor used in the superconducting magnet, and the cross-sectional dimensions of the second conductor are consistent with the cross-sectional dimensions of the conductor used in the superconducting magnet; The first insulation structure of the inter-conductor insulation layer is consistent with the second insulation structure of the inter-turn insulation layer, and an arc triggering element is embedded at the preset arc triggering position in the inter-conductor insulation layer.

[0007] Thus, the experimental prototype also includes a first conductor and a second conductor arranged parallel to each other. The cross-sectional dimensions of the first conductor and the second conductor are identical to those of the conductors used in superconducting magnets. The first insulation structure of the inter-conductor insulation layer matches the second insulation structure of the inter-turn insulation layer, and an arc-triggered element is pre-embedded at a predetermined arc-triggered position within the inter-conductor insulation layer. This ensures that the experimental prototype can realistically simulate the actual electrical and structural conditions between the turns of a superconducting magnet, giving the experimental results direct engineering reference value.

[0008] In some embodiments, the arc channel includes a plasma region that modulates the electric field strength and power characteristics of the initial arc by means of an equivalent thermal conductivity or a thermal conductivity scaling factor β.

[0009] Thus, the arc channel includes a plasma region, which adjusts the electric field strength and power characteristics of the initial arc through equivalent thermal conductivity or a thermal conductivity scaling factor β. In this way, simulating the initial arc through the plasma region allows for matching the electric field strength and power characteristics of a real arc, achieving efficient and accurate simulation of arc behavior. This lays the foundation for subsequent calculations under different insulation conditions and comparisons with experimental results.

[0010] In some implementations, the plasma region achieves an equivalent of the arc propagation process in the following way: Ignoring the radiation source term S in the arc heat conduction control equation, and introducing the thermal conductivity scaling factor β into the thermal conductivity term, we obtain the equivalent heat conduction control equation. The governing equation for arc heat conduction is: (1) The equivalent heat conduction control equation is: (2) Where ρ is the material density of the plasma, Cp is the specific heat capacity of the plasma at constant pressure, T is the current instantaneous temperature, t is time, r is the radial spatial coordinate, K is the original thermal conductivity of the plasma, σ is the electrical conductivity of the plasma, E is the electric field strength of the plasma, and S is the radiation source term.

[0011] In this way, by equating the arc propagation process in the plasma region of the arc channel to a heat conduction process, and by introducing a thermal conductivity scaling factor β to amplify the plasma thermal conductivity to achieve equivalent radiation and convection effects, the simulation calculation of the entire physical process of the arc plasma can be simplified.

[0012] In some embodiments, the thermal conductivity scaling factor β is a non-fixed value, adjusted during the simulation based on the experimental results of the electric arc test; the adjustment process includes: According to the different stages of the arc development process, a corresponding initial value of β is set for each stage. Numerical simulations were performed based on different β values ​​to obtain the corresponding simulation results; The simulation results are compared with the experimental results to determine the goodness of fit. When the simulation results and the experimental results meet the preset consistency conditions, the corresponding β parameter value is determined.

[0013] In this way, by calibrating the thermal conductivity scaling factor β in stages, the heat loss characteristics of different stages of arc development can be accurately matched, which simplifies the simulation calculation while ensuring the accuracy of arc behavior simulation.

[0014] In some embodiments, the different stages of the arc development process include a first stage in which the arc moves within the inter-turn insulation and a second stage in which the arc length increases after the conductor melts; the first stage and the second stage correspond to different β parameter values, and the β parameter value of the second stage is greater than the β parameter value of the first stage.

[0015] In this way, by adjusting the β parameter in stages, it is possible to achieve accurate simulation of the entire arc development cycle, ensuring a high degree of matching between simulation results and experimental results, and improving the accuracy of insulation and conductivity inversion.

[0016] In some embodiments, the conductivity sub-model includes a first type of sub-model and a second type of sub-model. The first type of sub-model is used to indicate that the simulated insulating element is a non-conductive element, and the second type of sub-model is used to indicate that the simulated insulating element is a conductive element. Each second type of sub-model corresponds to a set of independent conductivity sub-model parameters.

[0017] Thus, the conductivity sub-model includes a first type of sub-model and a second type of sub-model. The first type of sub-model indicates that the simulated insulating element is a non-conductive element, and the second type of sub-model indicates that the simulated insulating element is a conductive element. Each second type of sub-model corresponds to a set of independent conductivity sub-model parameters. In this way, through the first and second type of sub-models, it is possible to simulate different conductive states of insulating materials, thereby providing a basis for revealing the specific impact of insulation conductivity degradation on electric arcs.

[0018] In some implementations, each set of conductivity sub-model parameters includes the minimum conductivity of the simulated insulating element, the maximum conductivity of the simulated insulating element, the reference temperature at which the simulated insulating element is at the minimum conductivity, the transition temperature at which the conductivity of the simulated insulating element changes, and the transition temperature difference between the minimum conductivity and the maximum conductivity of the simulated insulating element.

[0019] Thus, each set of conductivity sub-model parameters includes the minimum conductivity of the simulated insulating element, the maximum conductivity of the simulated insulating element, the reference temperature at which the simulated insulating element reaches its minimum conductivity, the transition temperature at which the conductivity of the simulated insulating element changes, and the temperature difference between the minimum and maximum conductivity of the simulated insulating element. In this way, by establishing a standardized and physically meaningful conductivity model parameter system, a foundation can be provided for accurately simulating the conductive behavior of insulating materials during temperature changes.

[0020] In some implementations, the second type of sub-model is determined by the following relationship: ; in, The current instantaneous temperature of the simulated insulating element. The current instantaneous conductivity of the simulated insulating element at its current instantaneous temperature T. The minimum conductivity, The maximum conductivity, The Gaussian error function is... The reference temperature is... The transition temperature is... The transition temperature difference is the value mentioned above.

[0021] Thus, by quantifying the dynamic relationship between conductivity and temperature using a formula containing a Gaussian error function, the qualitative law that conductivity increases monotonically with temperature can be transformed into a quantitative calculation, making the simulation of the conductive behavior of insulating components more consistent with actual physical laws.

[0022] In some embodiments, the experimental simulation model includes an insulation coupling model and a conductivity coupling model. For the simulated insulating element in the benchmark simulation structure corresponding to the interconductor insulation layer of the experimental sample, multiple different conductivity sub-models are configured to obtain multiple experimental simulation models with different conductivity characteristics, including: The first type of sub-model is set for the simulated insulating element in the benchmark simulation structure to generate the insulation coupling model; Multiple second-type sub-models with different conductivity sub-model parameters are set for the simulated insulating element in the benchmark simulation structure to generate multiple conductive coupling models, wherein each conductive coupling model corresponds to one of the second-type sub-models.

[0023] Thus, a first-type sub-model is set for the simulated insulating element in the benchmark simulation structure to generate an insulation coupling model. Next, multiple second-type sub-models with different conductivity sub-model parameters are set for the simulated insulating element in the benchmark simulation structure to generate multiple conduction coupling models, where each conduction coupling model corresponds to one of the second-type sub-models. In this way, by constructing insulation coupling and conduction coupling models, it is possible to simulate different conductive states of insulating materials, thereby providing a foundation for revealing the specific impact of insulation conductivity degradation on electric arcs.

[0024] In some embodiments, the step of applying a preset DC current consistent with the arc test to multiple experimental simulation models and determining multiple simulation results includes: The preset DC current is applied to the insulation coupling model and multiple conductive coupling models respectively to simulate and determine multiple simulation results. The preset DC current is a constant current. Each simulation result includes a first volt-ampere characteristic relationship, simulated conductor ablation characteristics, and simulated insulation layer damage characteristics.

[0025] Thus, a preset DC current was applied to the insulation coupling model and multiple conductive coupling models respectively, and multiple simulation results were determined. The preset DC current was a constant current. Each simulation result included the first volt-ampere characteristic relationship, simulated conductor ablation characteristics, and simulated insulation layer damage characteristics. By setting a unified preset DC current and making it constant, the comparability of simulation results from multiple experimental models can be ensured. Furthermore, the outputs of the first volt-ampere characteristic relationship, simulated conductor ablation characteristics, and simulated insulation layer damage characteristics can provide a basis for subsequent comparative evaluation.

[0026] In some embodiments, the experimental results include the second current-voltage characteristic relationship, conductor ablation characteristics, and insulation layer damage characteristics. The step of performing a goodness-of-fit analysis on multiple simulation results and experimental results, and selecting the target simulation model with the highest goodness of fit to the experimental sample from multiple experimental simulation models, includes: A goodness-of-fit analysis was performed on the second current-voltage characteristic relationship and each of the first current-voltage characteristic relationships to determine multiple first fitting results; A goodness-of-fit analysis was performed on the conductor ablation characteristics and each of the simulated conductor ablation characteristics to determine multiple second fitting results; A goodness-of-fit analysis was performed on the insulation layer damage characteristics and each simulated insulation layer damage characteristic to determine multiple third-fit results; Based on multiple first fitting results, multiple second fitting results, and multiple third fitting results, the target simulation model is determined from the insulating coupling model and multiple conductive coupling models.

[0027] Thus, goodness-of-fit analyses were performed on the second volt-ampere characteristic relationship and each first volt-ampere characteristic relationship to determine multiple first fitting results. Next, goodness-of-fit analyses were performed on the conductor ablation characteristics and each simulated conductor ablation characteristic to determine multiple second fitting results. Then, goodness-of-fit analyses were performed on the insulation layer damage characteristics and each simulated insulation layer damage characteristic to determine multiple third fitting results. Finally, based on the multiple first fitting results, multiple second fitting results, and multiple third fitting results, a self-insulation coupling model and multiple conduction coupling models were used to determine the target simulation model. In this way, through multi-dimensional goodness-of-fit analyses of the volt-ampere characteristic relationship, ablation characteristics, and damage characteristics, it can be ensured that the target simulation model highly matches the experimental results in both the volt-ampere characteristic relationship and ablation characteristics, thereby enabling the selected target simulation model to reflect the conductive behavior of the arc and the inter-turn insulation layer of the superconducting magnet.

[0028] In some implementations, evaluating the conductivity behavior of the inter-turn insulation layer based on the conductivity sub-model corresponding to the target simulation model includes: Based on the conductivity sub-model corresponding to the target simulation model, the conductivity characteristics of the inter-turn insulation layer under the action of the initial electric arc are determined in order to analyze the influence of insulation conductivity degradation on arc behavior.

[0029] Thus, based on the conductivity sub-model corresponding to the target simulation model, the conductivity characteristics of the inter-turn insulation layer under the initial arc are determined to analyze the impact of insulation conductivity degradation on arc behavior. This allows for a quantitative assessment of the actual impact of insulation conductivity degradation on arc behavior, providing a foundation for short-circuit arc risk assessment in superconducting magnets.

[0030] This application also provides a computer device in which a computer program is stored in a memory, and when the processor executes the computer program, it implements the steps of the above method.

[0031] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described method.

[0032] Additional aspects and advantages of embodiments of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of embodiments of this application. Attached Figure Description

[0033] The above and additional aspects and advantages of this application will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 This is one of the flowcharts illustrating the evaluation method of certain embodiments of this application; Figure 2 This is a three-dimensional structural schematic diagram of an experimental sample for certain embodiments of this application; Figure 3 This is a cross-sectional structural diagram of an experimental sample for certain embodiments of this application; Figure 4 This is a schematic diagram illustrating the development process of an inter-turn short-circuit arc in a superconducting magnet according to certain embodiments of this application; Figure 5 This is a second flowchart illustrating the evaluation method of certain embodiments of this application; Figure 6 This is the third flowchart illustrating the evaluation method of certain embodiments of this application; Figure 7 This is the fourth flowchart illustrating the evaluation method of some embodiments of this application; Figure 8 This is the fifth flowchart illustrating the evaluation method of certain embodiments of this application. Detailed Implementation

[0034] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the embodiments of this application, and should not be construed as limiting the embodiments of this application.

[0035] During long-term operation or sudden quenching of a superconducting magnet, the inter-turn insulation layer may experience a short-circuit arc due to local defects, voltage surges, or other factors. Under the thermal effect of the arc, the conductivity of the inter-turn insulation layer degrades from an insulating state to a conductive state. Specifically, quenching refers to the sudden loss of superconductivity in a superconducting magnet due to factors such as abnormal local temperature increases or current overload, instantaneously transitioning from a zero-resistance state to a resistive state. This process is accompanied by a violent energy release and a sudden temperature rise. As a barrier isolating adjacent conductors, the inter-turn insulation layer may be broken down during quenching due to local defects or voltage surges, forming a short-circuit arc. This short-circuit arc is essentially a high-temperature plasma channel, with a core temperature reaching thousands or even tens of thousands of degrees Celsius, releasing intense thermal radiation and shock waves.

[0036] Under the sustained thermal effect of the electric arc, the microstructure of the inter-turn insulation layer undergoes irreversible damage, causing its conductivity to gradually degrade from an initial high-resistance insulation state to a low-resistance conductivity state. This degradation in conductivity may alter the combustion and propagation path of the electric arc, thus affecting the safe operation of the superconducting magnet. On one hand, the increased conductivity of the degraded inter-turn insulation layer leads to arc path instability, resulting in arc instability or extinction, thus affecting the safe operation of the superconducting magnet. On the other hand, the distribution of conductive regions alters the spatial distribution of the electric field intensity, guiding the arc away from its original propagation path. This may lead to excessive local energy concentration, exacerbating secondary damage such as conductor ablation and large-area damage to the inter-turn insulation layer, further impacting the safe operation of the superconducting magnet.

[0037] However, in related technologies, it is often difficult to directly obtain the conductivity characteristics of the inter-turn insulation layer under actual operating conditions. On the one hand, the operating environment of superconducting magnets is extremely complex, with multiple factors such as strong electromagnetic interference, drastic temperature differences between ultra-low and high-temperature arcs, and high pressure superimposed, making it difficult to stably deploy sensors and capture changes in conductivity parameters during the degradation process of the inter-turn insulation layer in real time. On the other hand, the degradation of the conductivity characteristics of the inter-turn insulation layer is a dynamic and non-uniform process. Its conductivity changes non-linearly with temperature, arc duration, and the degree of local damage, making it impossible to comprehensively characterize it through measurement data at a single time point or location. As a result, it is impossible to accurately determine the specific impact of the degradation of the inter-turn insulation layer's conductivity characteristics on arc behavior. It is impossible to quantify the correlation between the degree of degradation and arc stability and propagation path, and it is also difficult to establish a reliable arc fault evolution model. Ultimately, this makes the risk assessment of arc faults in superconducting magnets lack a scientific and accurate basis.

[0038] Based on the above issues, please refer to Figure 1 This application provides a method for evaluating the conductivity behavior of the inter-turn insulation layer of a superconducting magnet during short-circuit arc propagation. The method includes: 01: Construct a benchmark simulation structure that matches the geometry of the experimental sample; 02: For the simulated insulating element in the benchmark simulation structure that corresponds to the conductor insulation layer of the experimental sample, multiple different conductivity sub-models are configured to obtain multiple experimental simulation models with different conductivity characteristics; 03: Apply a preset DC current consistent with the electric arc test to multiple experimental simulation models respectively, and determine multiple simulation results; 04: Perform a goodness-of-fit analysis on multiple simulation results and experimental results, and select the target simulation model with the highest goodness of fit to the experimental sample from multiple experimental simulation models; 05: Evaluate the conductivity behavior of the inter-turn insulation layer based on the conductivity sub-model corresponding to the target simulation model.

[0039] This application also provides a computer device, including a memory and a processor. The method for evaluating the conductivity behavior of the inter-turn insulation layer of a superconducting magnet during short-circuit arc propagation, as described in this application, can be implemented by the computer device described in this application. Specifically, the memory stores a computer program, and the processor is used to construct a benchmark simulation structure consistent with the geometry of the experimental sample. For the simulated insulating elements in the benchmark simulation structure corresponding to the inter-conductor insulation layer of the experimental sample, multiple different conductivity sub-models are configured to obtain multiple experimental simulation models with different conductivity characteristics. A preset DC current consistent with the arc test is applied to each of the multiple experimental simulation models to determine multiple simulation results. The processor is also used to perform a goodness-of-fit analysis on the multiple simulation results and experimental results, and to select the target simulation model with the highest goodness of fit to the experimental sample from the multiple experimental simulation models. The conductivity behavior of the inter-turn insulation layer is evaluated based on the conductivity sub-model corresponding to the target simulation model.

[0040] Specifically, a superconducting magnet refers to a high-performance magnet built based on the zero-resistance properties of superconducting materials, including superconducting coils and insulating layers between conductors. The superconducting coil is made of superconducting wire and typically has a multi-turn structure.

[0041] Inter-turn insulation refers to the insulation structure used to isolate adjacent superconducting wires in a superconducting magnet. It can prevent electrical short circuits between adjacent superconducting wires, thereby ensuring the safe and stable operation of the superconducting magnet.

[0042] Conductivity refers to the evolution of the insulation state of the inter-turn insulation layer under the transient high temperature of a short-circuit arc, and the influence of this evolution on the arc initiation, propagation, stable combustion, and extinction behavior. For example, the dynamic process by which the inter-turn insulation layer gradually transforms from an initial insulating state to a conductive state through pyrolysis and carbonization.

[0043] Experimental specimens refer to standardized test pieces designed and manufactured to simulate the core structure and working conditions of real superconducting magnets. Their structure, materials, and dimensions are all matched to those of actual superconducting magnets.

[0044] Arc testing refers to the process of applying a constant DC current to a test sample in a controlled, room-temperature, inert gas environment, triggering a short-circuit arc at a preset location, simultaneously acquiring voltage and current signals, and observing the arc development process and the ablation morphology of the conductor and insulation layer.

[0045] The simulated arc triggering position refers to the spatial coordinates in the benchmark simulation structure that precisely correspond to the position of the arc triggering element embedded in the experimental sample.

[0046] The arc channel refers to the virtual region in the benchmark simulation model used to simulate the actual short-circuit arc. The arc is essentially a plasma conductive channel formed by the ionization of gas. Therefore, the arc channel must have electrical and thermal conductivity characteristics that match those of the actual plasma.

[0047] The preset arc triggering position refers to a fixed position determined in advance in the insulation layer between conductors. It is usually selected in the middle area along the length of the insulation layer to ensure that the arc can propagate evenly to both ends and avoid interference from end effects.

[0048] The initial arc refers to the arc generated by the melting of the triggering element and is in its early stages of development. Its location, power, electric field strength, and other characteristics have a decisive influence on the propagation path and stable combustion of the subsequent arc.

[0049] Simulated insulating elements refer to simulated components in finite element models that correspond to the insulating layer between conductors in experimental samples. Their material properties and geometric dimensions are consistent with those of the actual insulating layer between conductors, and they are used to simulate the electrical and thermal behavior of the actual insulating layer.

[0050] The conductivity sub-model refers to a mathematical model that describes the conductive properties of a simulated insulating element. Different sub-models correspond to different conductive states of the insulation, including a non-conductive state and a conductivity state that varies with temperature. This sub-model determines the logic of how the simulated insulation degradation behavior of the insulating element affects the arc behavior in the experimental simulation model. In this way, by setting multiple conductivity values ​​with different conductivity characteristics, all possible states of the simulated insulation layer, from non-conductive to highly conductive, can be covered. This provides sufficient experimental simulation model samples for subsequent evaluation of conductivity behavior, avoiding evaluation bias caused by a single experimental simulation model.

[0051] Experimental simulation models refer to multiple finite element models formed by assigning different conductivity sub-models to the simulated insulating elements in the benchmark simulation structure. Each experimental simulation model corresponds to an insulation and conductivity state assumption, which is used to cover insulation and conductivity characteristics under different degrees of degradation.

[0052] The preset DC current refers to the pre-set constant DC current loading condition. The value of the constant DC current is determined based on the current characteristics of the superconducting magnet under actual operation or fault conditions. It is applied to the experimental sample and experimental simulation model to simulate the real current conditions.

[0053] The simulation results refer to the simulation calculation output of each experimental simulation model under a preset DC current.

[0054] The experimental results refer to the actual data obtained after applying a preset DC current to the experimental sample.

[0055] The target simulation model refers to the experimental simulation model that best fits the experimental current-voltage characteristics and ablation features by comparing experimental results with simulation results corresponding to multiple sets of different conductivity. Its corresponding conductivity sub-model can reflect the actual conductive behavior of the superconducting magnet after the insulation of the inter-turn insulation layer degrades.

[0056] A benchmark simulation structure with the same geometry as the experimental sample is constructed, i.e., the benchmark simulation structure is established according to the geometric parameters of the experimental sample, such as conductor dimensions and insulation layer thickness. This ensures that the current density, electric field strength, and heat transfer path in the benchmark simulation structure match those of the arc test. Simultaneously, the arc channel must be precisely set at a position corresponding to the preset arc triggering position on the experimental sample to ensure that the initial arc initiation conditions are consistent.

[0057] Next, multiple sets of experimental simulation models are generated. Different conductivity sub-models are set for the simulated insulating elements in the benchmark simulation structure, including insulation coupling models that characterize good insulation and conductive coupling models that characterize insulation degradation, thus forming multiple sets of experimental simulation models with different conductivity characteristics.

[0058] Subsequently, the same preset DC current as in the arc test was applied to each experimental simulation model, and multi-dimensional simulation results, including electrical characteristics and physical damage, were calculated. Each simulation result corresponds to one experimental simulation model.

[0059] Then, a goodness-of-fit analysis was performed on multiple simulation results and experimental results to select the target simulation model with the highest goodness of fit from multiple experimental simulation models. Specifically, a preset DC current was applied to the experimental sample to trigger the element to melt and initiate an arc. Voltage and current signals during the arc combustion process were collected, and the ablation characteristics of the conductor and insulation layer were observed after the experiment. At the same time, the same preset DC current was applied to multiple sets of experimental simulation models, and the voltage distribution, electric field intensity distribution, and ablation characteristics of each set of models were calculated to obtain multiple sets of simulation results. The volt-ampere characteristics and ablation characteristics obtained from the experiment were compared with each set of simulation results one by one. Through goodness-of-fit analysis, the target simulation model with the highest goodness of fit was selected. The conductivity sub-model corresponding to this target simulation model is the equivalent conductivity characteristic after the inter-turn insulation degrades. Based on this conductivity sub-model, the influence of insulation conductivity behavior on the stable combustion and propagation path of the arc can be quantitatively analyzed, and the conductivity behavior of the inter-turn insulation layer of the superconducting magnet can be evaluated.

[0060] Finally, based on the conductivity sub-model corresponding to the target simulation model, the conductivity behavior of the inter-turn insulation layer is evaluated, that is, the influence of insulation conductivity degradation on arc voltage, power, propagation speed and stable burning time is quantitatively analyzed, and it is determined whether insulation carbonization will lead to arc extinction or aggravate the severity of the fault.

[0061] In summary, a benchmark simulation structure with the same geometry as the experimental prototype was constructed. The experimental prototype was matched to the superconducting magnet and used for arc testing of the inter-turn insulation layer of the superconducting magnet. An arc channel was set at the simulated arc trigger position of the benchmark simulation structure, corresponding to the preset arc trigger position of the experimental prototype. The arc channel was used to simulate the initial arc. Next, multiple different conductivity sub-models were configured for the simulated insulating element in the benchmark simulation structure corresponding to the inter-conductor insulation layer of the experimental prototype, resulting in multiple experimental simulation models with different conductivity characteristics. Each experimental simulation model corresponds to a conductivity sub-model, which indicates the conductivity characteristics of the simulated insulating element in the experimental simulation model. Subsequently, a preset DC current consistent with the arc test was applied to each of the multiple experimental simulation models, and multiple simulation results were determined. Each simulation result corresponds to one experimental simulation model. Then, a goodness-of-fit analysis was performed on the multiple simulation results and experimental results. The target simulation model with the highest goodness of fit to the experimental prototype was selected from the multiple experimental simulation models, where the experimental results were obtained based on the arc test. Finally, the conductivity behavior of the inter-turn insulation layer is evaluated based on the conductivity sub-model corresponding to the target simulation model. This ensures the reliability of the experimental results and the authenticity of the conductivity behavior assessment by constructing an experimental prototype that matches the actual superconducting magnet structure. Furthermore, by configuring an experimental simulation model with the same geometry as the experimental prototype and setting multiple conductivity levels, the simulation model can comprehensively cover different conductivity states of the inter-turn insulation layer. By comparing and fitting the experimental results of the prototype with the simulation results of multiple experimental simulation models, the equivalent conductivity characteristics of the inter-conductor insulation layer after insulation degradation can be determined. This allows for a quantitative analysis of the impact of electric arc on the conductivity behavior of the insulation layer, ultimately providing a reliable basis for the risk assessment of short-circuit arcs in superconducting magnets.

[0062] Please see Figure 2 and Figure 3 In some embodiments, the experimental sample also includes a first conductor and a second conductor arranged parallel to each other; The cross-sectional dimensions of the first conductor are consistent with those of the conductor used in the superconducting magnet, and the cross-sectional dimensions of the second conductor are consistent with those of the conductor used in the superconducting magnet. The first insulation structure of the inter-conductor insulation layer is consistent with the second insulation structure of the inter-turn insulation layer, and an arc triggering element is embedded at the preset arc triggering position in the inter-conductor insulation layer.

[0063] Specifically, please refer to Figure 2 and Figure 3 ,in, Figure 2 This is a three-dimensional structural schematic diagram of experimental sample 100. Figure 3This is a cross-sectional structural diagram of experimental sample 100. In the diagram, 11 represents the first conductor, 12 represents the second conductor, 13 represents the inter-conductor insulation layer, 14 represents the arc triggering element, 15 represents the grounding insulation layer, and 16 represents the insulating filler block. The experimental sample includes a first conductor and a second conductor arranged parallel to each other, as well as an inter-conductor insulation layer.

[0064] The first conductor and the second conductor refer to the two parallel conductors that make up the experimental sample. The cross-sectional dimensions of the first conductor and the second conductor are consistent with those of the conductors used in the superconducting magnet. They are used to simulate the structure of adjacent conductors in the superconducting magnet and to ensure the correlation between the experimental sample and the actual superconducting magnet.

[0065] The inter-conductor insulation layer refers to the insulation structure located between the first and second conductors. This inter-conductor insulation layer conforms to the second insulation structure of the inter-turn insulation layer actually used in superconducting magnets, meaning it maintains consistency in material composition, curing process, and electrical insulation function. The inter-conductor insulation layer possesses high-temperature resistance and electromagnetic environment resistance, serving to isolate the two conductors and prevent short circuits during normal operation. In some embodiments, both the inter-conductor insulation layer in the experimental prototype and the inter-turn insulation layer in the superconducting magnet use polyimide and glass fiber as the reinforcing insulating matrix, and are impregnated, heated, and cured using an epoxy resin vacuum pressure impregnation process. This ensures that the inter-conductor insulation layer in the experimental prototype can effectively simulate the behavior of the inter-turn insulation layer of a real superconducting magnet under fault conditions. It should be noted that if the second insulation structure of the inter-turn insulation layer is changed, the inter-conductor insulation layer will also be adjusted accordingly.

[0066] The first insulation structure refers to the description of the composition and molding process of the insulation layer material between conductors.

[0067] The conductors used in superconducting magnets refer to the conductive components actually applied to superconducting magnets. They have specific cross-sectional dimensions and material requirements and are capable of generating and maintaining a magnetic field.

[0068] Arc triggering elements refer to fusible metal components that are pre-embedded in the insulation layer between conductors at predetermined arc triggering positions. They can melt through resistance heating after the experimental sample is energized, accurately triggering the initial short-circuit arc, ensuring the repeatability of the test and the controllability of the arc initiation position.

[0069] Thus, the experimental prototype also includes a first conductor and a second conductor arranged parallel to each other. The cross-sectional dimensions of the first conductor and the second conductor are identical to those of the conductors used in superconducting magnets. The first insulation structure of the inter-conductor insulation layer matches the second insulation structure of the inter-turn insulation layer, and an arc-triggered element is pre-embedded at a predetermined arc-triggered position within the inter-conductor insulation layer. This ensures that the experimental prototype can realistically simulate the actual electrical and structural conditions between the turns of a superconducting magnet, giving the experimental results direct engineering reference value.

[0070] In some embodiments, the arc channel includes a plasma region that modulates the electric field strength and power characteristics of the initial arc by means of an equivalent thermal conductivity or a thermal conductivity scaling factor β.

[0071] Specifically, the physical essence of a real electric arc is a high-temperature plasma state. The formation and propagation of this real plasma region are accompanied by complex electromagnetic and thermal coupling effects, including multiple physical phenomena such as ionization, radiation, convection, and conduction. If we directly model the entire physical process of the real plasma region, we not only need to consider a large number of microscopic physical mechanisms, but also face the problems of extremely large computational load and difficulty in accurately setting boundary conditions.

[0072] In this embodiment, a dedicated arc channel, i.e., a plasma region, is set in the benchmark simulation structure to equivalently replace the physical carrier of the real arc, i.e., the initial arc. Then, the equivalent thermal conductivity or scaling factor can be used as an adjustment means to calibrate the thermal and electrical characteristics of the plasma region, thereby matching the electric field strength and power characteristics of the real plasma region. This achieves efficient and accurate simulation of arc behavior, laying the foundation for subsequent calculations under different insulation conditions and comparisons with experimental results.

[0073] The electric arc channel simulates the conductive channel formed by ionized gas during electric arc combustion. It is the main path for current transmission and heat release, characterized by high temperature, high conductivity, and strong thermal radiation. The electric field strength and power characteristics of the initial electric arc directly determine the impact of the plasma region on the ablation and degradation of the insulating layer.

[0074] In one example, since the experimental environment is helium and the main component of the conductor in the experimental sample is stainless steel, the conductor may ablate during the arc combustion process, generating iron vapor that mixes with the surrounding helium. Therefore, the electrical and thermal conductivity of a helium-iron plasma mixture containing 10% helium by volume is selected to characterize the physical properties of the arc. In this way, the radiative heat loss of the arc is neglected, and its effect is compensated by introducing a thermal conductivity scaling factor β into the thermal conductivity. The combined effect of radiation and convection processes can be reflected in the heat conduction equation without the need for separate modeling of radiation and convection processes.

[0075] The thermal conductivity scaling factor β refers to the proportionality coefficient used to adjust the electrical or thermal parameters of the plasma region. It can be used to scale and calibrate key parameters in the electric field strength calculation equation or power transmission model according to the characteristics of the real plasma region, so as to match the energy output law of the real plasma region.

[0076] Electric field strength refers to a physical quantity that characterizes the strength of the electric field within the initial electric arc. It directly affects the conductivity and voltage distribution of the plasma region and is a parameter that determines whether the insulating layer is further broken down and whether the plasma region burns stably.

[0077] Power characteristics refer to the energy output and transfer patterns in the plasma region during combustion, including power density and energy decay rate. The magnitude of power characteristics directly determines the degree and extent of ablation of conductors and insulating layers.

[0078] Thus, the arc channel includes a plasma region, which adjusts the electric field strength and power characteristics of the initial arc through equivalent thermal conductivity or a thermal conductivity scaling factor β. In this way, simulating the initial arc through the plasma region allows for matching the electric field strength and power characteristics of a real arc, achieving efficient and accurate simulation of arc behavior. This lays the foundation for subsequent calculations under different insulation conditions and comparisons with experimental results.

[0079] In some implementations, the plasma region achieves an equivalent of the arc propagation process in the following way: Ignoring the radiation source term S in the electric arc heat conduction control equation, and introducing the thermal conductivity scaling factor β into the thermal conductivity term, we obtain the equivalent heat conduction control equation. The governing equation for arc heat conduction is: (1) The equivalent heat conduction governing equation is: (2) All of the above plasma parameters can be determined based on a helium-iron plasma mixture containing 10% helium by volume. The meanings of each physical quantity are as follows: ρ is the material density of the plasma, Cp is the specific heat capacity of the plasma at constant pressure, T is the current instantaneous temperature, t is time, r is the radial spatial coordinate, K is the original thermal conductivity of the plasma, σ is the electrical conductivity of the plasma, E is the electric field strength of the plasma, and S is the radiation source term.

[0080] Specifically, the arc heat conduction control equation (1), also known as the arc full physical energy conservation equation, is a basic partial differential equation describing the energy balance law in the arc plasma region, which can cover all core thermophysical processes in the arc propagation process.

[0081] The radiation source term S refers to the source term in the arc heat conduction governing equation that characterizes the energy transfer of the arc plasma outward through thermal radiation. It is a key parameter affecting the arc temperature field and electric field intensity distribution. The calculation of the radiation source term S requires consideration of a large number of microscopic parameters such as plasma emissivity, absorption coefficient, and temperature distribution, resulting in extremely high computational complexity.

[0082] The thermal conductivity scaling factor β refers to a dimensionless scaling factor used to amplify the original thermal conductivity of plasma. It converts the radiation and convection heat exchange effects, which originally needed to be modeled separately, into the heat conduction process, thus achieving a balance between equation simplification and physical reality.

[0083] The original thermal conductivity K refers to the inherent thermal conductivity coefficient of the plasma material itself. It only characterizes the inherent ability of plasma to transfer heat through molecular thermal motion and corresponds only to the heat exchange form of heat conduction.

[0084] ρ is the material density of the plasma, characterizing the mass of the plasma per unit volume. Cp is the specific heat capacity at constant pressure, characterizing the heat required for a unit mass of plasma to increase its temperature by 1 K under constant pressure; it is a parameter describing the material's heat storage capacity. T is the current instantaneous temperature of the plasma region, a dynamic variable that varies with time and spatial location. t is time, the independent variable in the simulation process. r is the radial spatial coordinate; since the propagation of the electric arc in a confined space can be approximated as a cylindrically symmetric radial propagation process, cylindrical coordinates are used to simplify the modeling. σ is the electrical conductivity of the plasma, characterizing its ability to conduct electricity. E is the electric field strength of the plasma, characterizing the voltage drop per unit length, and determining the Joule heat generated by the electric arc.

[0085] In this way, by equating the arc propagation process in the plasma region of the arc channel to a heat conduction process, and by introducing a thermal conductivity scaling factor β to amplify the plasma thermal conductivity to achieve equivalent radiation and convection effects, the simulation calculation of the entire physical process of the arc plasma can be simplified.

[0086] In some implementations, the thermal conductivity scaling factor β is a non-fixed value, adjusted during the simulation based on the experimental results of the electric arc test; the adjustment process includes: According to the different stages of the arc development process, a corresponding initial value of β is set for each stage. Numerical simulations were performed based on different β values ​​to obtain the corresponding simulation results; The simulation results are compared with the experimental results to determine the goodness of fit. When the simulation results and experimental results meet the preset consistency conditions, the corresponding β parameter value is determined.

[0087] Specifically, the different stages of electric arc development refer to the different physical stages in the entire life cycle of an electric arc, from its initial ignition to its eventual extinction, due to fundamental changes in arc morphology, conductor state, and heat exchange characteristics. These stages include two phases: The first phase is the small arc stage, where the arc moves within the inter-turn insulation layer, corresponding to the process from arc ignition to conductor melting. In this phase, the effective arc radius is small, and heat exchange with the external environment is weak. The second phase is the large arc stage, where the arc length increases after conductor melting, corresponding to the process from conductor melting to arc extinction. In this phase, the effective arc radius is large, and heat exchange with the external environment is strong. The heat loss characteristics of the two phases are fundamentally different.

[0088] The initial β value refers to the pre-set β reference value for the basic thermal characteristics of different stages of arc development. It serves as the reference range for subsequent simulations. Based on the physical characteristics of the arc stage, it can significantly reduce the parameter range of subsequent simulations and improve calibration efficiency.

[0089] Numerical simulation refers to solving the equivalent heat conduction control equations with different β values ​​based on the finite element method, and completing the electro-thermal coupling simulation calculation of the arc propagation process.

[0090] Preset consistency conditions refer to the pre-set quantization threshold used to determine the degree of matching between simulation results and experimental data. It is the criterion for determining the optimal β parameter and ensuring that the calibrated arc model meets the simulation accuracy requirements.

[0091] Based on the physical evolution of electric arcs, the entire life cycle of an electric arc is divided into multiple stages with different heat exchange characteristics. Then, according to the heat loss characteristics of each stage, a corresponding initial value of β is set for the experimental simulation model. For example, in the small arc stage, where heat loss is weak, the initial value of β can be set to 1~2; in the large arc stage, where heat loss is strong, the initial value of β can be set to 1.5~4. By setting the initial value reasonably, the range of subsequent parameter traversal is significantly reduced, and the calibration efficiency is improved.

[0092] Next, using the initial value set in the first step as a baseline, β is adjusted within a reasonable range based on the differences between the simulation and experimental results, thereby obtaining multiple sets of different β values ​​for controlled variable simulation. That is, each set of experimental simulation models only changes the β parameter, while the remaining geometric structure, material parameters, current loading conditions, and boundary environment are completely consistent with the electric arc test, ensuring that β is the only variable, eliminating the interference of other factors on the simulation results, and obtaining multiple sets of simulation results.

[0093] Then, the multiple sets of simulation results obtained in the second step are quantitatively fitted and matched with the experimental data measured in the arc test. For example, for the voltage waveform, the curve overlap is calculated using methods such as the Pearson correlation coefficient; for the conductor ablation morphology, the relative errors of parameters such as ablation length and maximum ablation depth are calculated. When the simulation results corresponding to a certain set of β simultaneously meet the preset consistency conditions, such as the voltage waveform correlation coefficient ≥ 0.80 (which can be adaptively adjusted according to the actual experimental accuracy), and the relative error of the ablation parameters ≤ 10%, then that set of β is determined to be the optimal parameter value after calibration.

[0094] In this way, by calibrating the thermal conductivity scaling factor β in stages, the heat loss characteristics of different stages of arc development can be accurately matched, which simplifies the simulation calculation while ensuring the accuracy of arc behavior simulation.

[0095] In some implementations, the arc development process includes a first stage in which the arc moves within the inter-turn insulation and a second stage in which the arc length increases after the conductor melts; the first stage and the second stage correspond to different β parameter values, and the β parameter value of the second stage is greater than the β parameter value of the first stage.

[0096] Specifically, the first stage, also known as the small arc stage, refers to the arc development stage from the moment the arc is triggered until the conductor melts. The physical characteristics of this first stage are: the arc is strictly confined within the gap of the inter-turn insulation layer between two parallel conductors; the effective arc radius is small, the arc length is short, the contact area with the surrounding inert gas environment is limited, heat exchange is mainly through heat conduction between plasma and conductors and insulation layers, the heat loss from convection and thermal radiation accounts for a very small proportion, and the overall heat loss intensity is weak.

[0097] The second stage, also known as the large arc stage, refers to the arc development stage from the moment the conductor melts and breaks until the arc finally extinguishes. The physical characteristics of this second stage are: the conductor melts and breaks under the continuous heat of the arc, creating gaps in the original parallel conductor structure; the arc's combustion path is significantly lengthened; the effective arc radius increases significantly; the contact area with the surrounding inert gas environment increases dramatically; and in addition to basic heat conduction, the proportion of heat loss from convection and thermal radiation increases significantly, resulting in an overall heat loss intensity far exceeding that of the first stage.

[0098] Please see Figure 4 , Figure 4 This diagram illustrates the short-circuit arc fault evolution of the inter-turn insulation layer in a superconducting magnet, showcasing two possible fault development paths under the thermal effects of an arc. Figure 4 The upper right corner shows an enlarged view of the cross-sectional structure of the superconducting magnet winding. From the inside out, the winding consists of a conductor, an inter-turn insulation layer, and a ground insulation layer. The experimental sample of the embodiment of this application is designed based on the actual winding structure of the superconducting magnet. Figure 4The upper left corner shows the first stage of arc development. After energization, an initial inter-turn arc is triggered at the preset arc trigger position in the inter-turn insulation layer. At this time, the arc propagates within the inter-turn insulation layer between two adjacent parallel conductors, and the current forms a loop between the two conductors through the arc channel. Under the thermal effect of the arc, the inter-turn insulation layer may exhibit two completely different fault development paths: like Figure 4 The evolution path of non-conductive insulation shown in the lower left corner shows that if the inter-turn insulation layer still lacks conductivity after degrading under the heat of the electric arc, the electric arc will continue to burn stably and continuously erode the conductor, eventually causing the conductor to melt and break, and the arc burning path will be greatly lengthened.

[0099] like Figure 4 The insulation carbonization and conduction evolution path shown in the lower right corner indicates that if the inter-turn insulation layer undergoes pyrolysis and carbonization under the heat of the electric arc and forms a continuous conductive channel, the current will mainly flow through the carbonized insulation layer, and the original electric arc channel will be extinguished due to current diversion.

[0100] In this way, by adjusting the β parameter in stages, it is possible to achieve accurate simulation of the entire arc development cycle, ensuring a high degree of matching between simulation results and experimental results, and improving the accuracy of insulation and conductivity inversion.

[0101] In some implementations, the conductivity sub-model includes a first type of sub-model and a second type of sub-model. The first type of sub-model is used to indicate that the simulated insulating element is a non-conductive element, and the second type of sub-model is used to indicate that the simulated insulating element is a conductive element. Each second type of sub-model corresponds to a set of independent conductivity sub-model parameters.

[0102] Specifically, the first type of sub-model refers to a type of conductivity sub-model, which is used to indicate that the simulated insulating element is in a completely insulating and non-conductive state. Its resistivity value is set to be extremely high, which can be approximated as the inability of current to pass through, and is used to simulate the intact insulation characteristics that have not degraded.

[0103] The second type of sub-model refers to another category of conductivity sub-models, used to indicate the conductive state of simulated insulating elements and to simulate the conductivity of insulation components after degradation under the heat of an electric arc. In actual working conditions, an electric arc generates a strong thermal effect, causing the temperature of the surrounding insulating material to rise continuously. This temperature rise damages the molecular structure of the insulating material, leading to a decrease in its insulation performance and an increase in its conductivity. The higher the temperature, the more severe the damage and the stronger the conductivity. The second type of sub-model quantifies this law, enabling the simulation results to realistically reproduce the dynamic process of insulation conductivity degradation, thereby improving the realism and accuracy of the experimental simulation model.

[0104] The conductivity sub-model parameters are physical quantities used to distinguish different second-type sub-models and can quantify the conductivity characteristics of simulated insulating elements. The conductivity sub-model parameters include the minimum conductivity of the simulated insulating element, the maximum conductivity of the simulated insulating element, the reference temperature at which the simulated insulating element reaches its minimum conductivity, the transition temperature at which the conductivity characteristics of the simulated insulating element change, and the temperature difference between the minimum and maximum conductivity of the simulated insulating element.

[0105] Thus, the conductivity sub-model includes a first type of sub-model and a second type of sub-model. The first type of sub-model indicates that the simulated insulating element is a non-conductive element, and the second type of sub-model indicates that the simulated insulating element is a conductive element. Each second type of sub-model corresponds to a set of independent conductivity sub-model parameters. In this way, through the first and second type of sub-models, it is possible to simulate different conductive states of insulating materials, thereby providing a basis for revealing the specific impact of insulation conductivity degradation on electric arcs.

[0106] In some implementations, each set of conductivity sub-model parameters includes the minimum conductivity of the simulated insulating element, the maximum conductivity of the simulated insulating element, the reference temperature at which the simulated insulating element is at its minimum conductivity, the transition temperature at which the conductivity of the simulated insulating element changes, and the temperature difference between the minimum and maximum conductivity of the simulated insulating element.

[0107] Specifically, minimum conductivity This refers to the lowest conductivity that a simulated insulating element can exhibit. It corresponds to the conductivity value when the insulating material has not undergone significant degradation and is in a near-insulating state; it is the lower limit of the conductivity variation range. In some embodiments, the minimum conductivity of the polyimide-glass fiber composite insulating material used in this application can reach the GΩ level.

[0108] Maximum conductivity This refers to the highest conductivity achievable by a simulated insulating element under extreme high temperatures and severe degradation. It represents the upper limit of the conductivity variation range and is determined by the physical properties and high-temperature tolerance limit of the insulating material. In some embodiments, since the glass fiber in the polyimide-glass fiber composite insulating material used in this application maintains its insulating properties across the entire temperature range, the conductivity after carbonization is mainly determined by the polyimide matrix. Therefore, the minimum conductivity value can be determined by referring to the experimentally obtained test value of polyimide at 1000℃.

[0109] Reference temperature This refers to the fact that the conductivity of the simulated insulating element is exactly the minimum conductivity. The corresponding temperature is the critical temperature at which the insulating and conductive properties have not degraded; below this temperature, the insulating material essentially maintains its insulating state. In some embodiments, the reference temperature can be determined based on the operating temperature of the superconducting magnet.

[0110] Transition temperature This refers to the critical temperature at which the conductivity of a simulated insulating element undergoes a significant change. When the temperature reaches or approaches this temperature, the conductivity begins to increase rapidly, marking the transition from weak to strong conductivity in the insulation. In some implementations, the transition temperature can be determined based on the characteristic temperature at which polyimide undergoes violent pyrolysis.

[0111] transition temperature difference This refers to characterizing conductivity from arrive The width of the temperature range and the magnitude of the value determine the smoothness of the conductivity increase process. The smaller the value, the steeper the increase in conductivity. The larger the value, the smoother the growth process, which is used to accommodate the different degradation rates of different insulating materials. In some embodiments, the transition temperature difference can be determined based on the temperature range characteristics of polyimide from the start of pyrolysis to complete carbonization.

[0112] Thus, each set of conductivity sub-model parameters includes the minimum conductivity of the simulated insulating element, the maximum conductivity of the simulated insulating element, the reference temperature at which the simulated insulating element reaches its minimum conductivity, the transition temperature at which the conductivity of the simulated insulating element changes, and the temperature difference between the minimum and maximum conductivity of the simulated insulating element. In this way, by establishing a standardized and physically meaningful conductivity model parameter system, a foundation can be provided for accurately simulating the conductive behavior of insulating materials during temperature changes.

[0113] In some implementations, the second type of sub-model can be determined by the following relationship: ; in, To simulate the current instantaneous temperature of the insulating component, To simulate the current instantaneous conductivity of an insulating element at its current instantaneous temperature T, For minimum conductivity, For maximum conductivity, The Gaussian error function is... As the reference temperature, To change the temperature, This represents the transition temperature difference.

[0114] Specifically, the second type of sub-model mentioned above adopts a smooth interpolation-type empirical model constructed using the Gaussian error function erf, which is commonly used for describing the conductivity transition in numerical simulations of electric arcs, plasmas, and phase transition processes. It should be noted that the advantage of this smooth interpolation-type empirical model lies in its continuous S-shaped variation characteristics, which can characterize the gradual evolution of the polyimide-glass fiber composite insulation material in this invention from an initial low-conductivity insulating state to a high-temperature high-conductivity degenerate state under the transient high temperature of an electric arc. This ensures the continuity of the conductivity physical quantity across the entire temperature range and effectively improves the stability of finite element numerical calculations, avoiding the non-smoothness and non-convergence problems that may occur when using piecewise functions to describe abrupt changes in conductivity.

[0115] The current instantaneous temperature T refers to the actual temperature of the simulated insulating element at a certain moment during the simulation process. It is determined by the arc heating effect, heat conduction and other processes, and is a dynamic input variable for conductivity calculation, which is updated in real time as the simulation progresses.

[0116] Current instantaneous conductivity It refers to the quantified value of the conductivity of the simulated insulating element at the current instantaneous temperature T. It is calculated by the relationship and is adjusted in real time as the temperature T changes. It is the core output quantity that reflects the dynamic degradation state of the insulation.

[0117] Gaussian error function This refers to a common, continuously smooth function whose value ranges from -1 to 1, exhibiting a monotonically increasing property, and is used to express conductivity in a relational expression. arrive The smooth transition conforms to the actual degradation pattern of insulating materials.

[0118] Thus, by quantifying the dynamic relationship between conductivity and temperature using a formula containing a Gaussian error function, the qualitative law that conductivity increases monotonically with temperature can be transformed into a quantitative calculation, making the simulation of the conductive behavior of insulating components more consistent with actual physical laws.

[0119] Please see Figure 5 In some implementations, the experimental simulation model includes an insulating coupling model and a conductive coupling model, and step 02 includes: 021: Set the first type of sub-model for the simulated insulating elements in the benchmark simulation structure to generate an insulation coupling model; 022: Set up multiple second-class sub-models with different conductivity sub-model parameters for the simulated insulating elements in the benchmark simulation structure to generate multiple conductive coupling models.

[0120] In some implementations, the processor is also configured to set a first type of sub-model for the simulated insulating elements in the benchmark simulation structure to generate an insulation coupling model, and to set a second type of sub-model with different conductivity sub-model parameters for the simulated insulating elements in the benchmark simulation structure to generate a plurality of conductive coupling models.

[0121] Specifically, the insulation coupling model refers to the experimental simulation model generated by configuring the first type of sub-model onto the simulated insulating element, used to simulate the arc behavior when the insulation is intact. In this insulation coupling model, current can only flow between the two conductors through the arc channel, and the insulating layer does not participate in the conduction process.

[0122] A conductive coupling model refers to an experimental simulation model generated by configuring a second-type sub-model onto a simulated insulating element. Each conductive coupling model corresponds to a specific set of conductivity sub-model parameters, used to simulate conductive conditions under different degrees of insulation degradation. If the conductivity sub-model parameters in the second-type sub-model are different, then the second-type sub-model is different, and the corresponding conductive coupling model is also different. For example, adjusting the maximum conductivity parameter of the second-type sub-model from 1000 S / m to 10000 S / m creates two different second-type sub-models, which in turn generate two conductive coupling models with different conductivity characteristics, simulating scenarios of mild and severe insulation degradation, respectively.

[0123] First, a baseline simulation structure was constructed, ensuring its geometry was consistent with the experimental sample and included the arc channel. This baseline simulation structure provides uniform geometric and material parameters, ensuring that the subsequently generated insulation coupling model and multiple conductive coupling models differ only in simulating the conductivity characteristics of the insulating element, while remaining identical in all other aspects.

[0124] Next, the first type of sub-model is configured into the simulated insulating element in the benchmark simulation structure to generate an insulation coupling model. At the same time, by adjusting the conductivity parameters of the second type of sub-model, such as changing the maximum conductivity and transition temperature, multiple sets of second type sub-models with different parameters are constructed and configured into the simulated insulating element in the benchmark simulation structure to generate multiple conductive coupling models covering different degrees of insulation degradation.

[0125] Thus, a first-type sub-model is set for the simulated insulating element in the benchmark simulation structure to generate an insulation coupling model. Next, multiple second-type sub-models with different conductivity sub-model parameters are set for the simulated insulating element in the benchmark simulation structure to generate multiple conduction coupling models, where each conduction coupling model corresponds to one of the second-type sub-models. In this way, by constructing insulation coupling and conduction coupling models, it is possible to simulate different conductive states of insulating materials, thereby providing a foundation for revealing the specific impact of insulation conductivity degradation on electric arcs.

[0126] Please see Figure 6In some implementations, step 03 includes: 031: Apply a preset DC current to the insulation coupling model and multiple conductive coupling models respectively, and determine multiple simulation results.

[0127] In some implementations, the processor is also used to simulate applying a preset DC current to the insulating coupling model and multiple conductive coupling models respectively, and to determine multiple simulation results.

[0128] Specifically, the preset DC current is a constant current, which can keep the current value stable throughout the simulation process and does not change with time or temperature.

[0129] The simulation results refer to the simulation calculation output of the experimental simulation model under a preset DC current, which can characterize the arc behavior and the data corresponding to the insulation degradation behavior of the simulated insulating elements included in the experimental simulation model, including the first volt-ampere characteristic relationship, the simulated conductor ablation characteristics and the simulated insulation layer damage characteristics, which can provide a basis for comparison with experimental results.

[0130] Among them, the first voltage-current characteristic relationship refers to the relationship between voltage and current changes over time obtained by simulation calculations of various experimental simulation models, namely the insulation coupling model and multiple conductive coupling models, after applying a preset DC current. It is presented in the form of curves or data sets and can reflect the electrical characteristics in the arc development process.

[0131] Simulated conductor ablation characteristics refer to the damage characteristics of a conductor under the thermal effect of an electric arc, obtained from simulations based on various experimental models. These characteristics include the length, depth, width, and morphology of the ablation, as well as parameters such as conductor mass loss, remaining cross-sectional area, and the location and distribution of the ablation region. Conductor ablation is a direct manifestation of the thermal effect of the electric arc and can reflect the energy distribution and propagation path of the electric arc.

[0132] Simulated insulation layer damage characteristics refer to the damage features of the insulation layer under arc heating obtained from various experimental simulation models. These characteristics include parameters such as the size, shape, and depth of the carbonized region, the extent of the pyrolysis region, the remaining thickness of the insulation layer, and the location and distribution of the damaged region. Insulation layer damage characteristics directly reflect the degree of thermal degradation and changes in the electrical conductivity of the insulating material.

[0133] During simulation data processing, after applying a constant DC current to each experimental simulation model, the model solves the electro-thermal coupling control equations and calculates the changes in current and temperature distribution over time within the entire simulation domain. At each time step, the model records the voltage between the two conductors, forming the first volt-ampere characteristic relationship. Simultaneously, the model records the temperature distribution of the conductors; when the temperature exceeds the conductor's melting point, the unit is marked as an ablation unit. The number, location, and volume of ablation units are counted, and the length, depth, and mass loss of the ablation are calculated, forming the simulated conductor ablation characteristics. Furthermore, the model records the temperature distribution of the insulation layer; when the temperature exceeds the pyrolysis temperature of the insulation material, the unit is marked as a pyrolysis unit; when the temperature exceeds the carbonization temperature, it is marked as a carbonization unit. The number, location, and volume of pyrolysis and carbonization units are counted, and the size and depth of the carbonization region are calculated, forming the simulated insulation layer damage characteristics.

[0134] Thus, a preset DC current was applied to the insulation coupling model and multiple conductive coupling models respectively, and multiple simulation results were determined. The preset DC current was a constant current. Each simulation result included the first volt-ampere characteristic relationship, simulated conductor ablation characteristics, and simulated insulation layer damage characteristics. By setting a unified preset DC current and making it constant, the comparability of simulation results from multiple experimental simulation models can be ensured. Furthermore, the outputs of the first volt-ampere characteristic relationship, simulated conductor ablation characteristics, and simulated insulation layer damage characteristics can provide a basis for subsequent comparative evaluation.

[0135] Please see Figure 7 In some embodiments, the experimental results include the second current-voltage characteristic relationship, conductor ablation characteristics, and insulation layer damage characteristics. Step 04 includes: 041: Perform goodness-of-fit analysis on the second current-voltage characteristic relationship and each first current-voltage characteristic relationship respectively, and determine multiple first fitting results; 042: Perform fit analysis on the conductor ablation characteristics and each simulated conductor ablation characteristics to determine multiple second fit results; 043: Perform fit analysis on the insulation layer damage characteristics and each simulated insulation layer damage characteristics to determine multiple third-fit results; 044: Based on multiple first fitting results, multiple second fitting results, and multiple third fitting results, the target simulation model is determined using the self-insulating coupling model and multiple conductive coupling models.

[0136] In some embodiments, the processor is further configured to perform goodness-of-fit analysis on the second volt-ampere characteristic relationship and each first volt-ampere characteristic relationship respectively, to determine multiple first fitting results. It is also configured to perform goodness-of-fit analysis on the conductor ablation characteristics and each simulated conductor ablation characteristics respectively, to determine multiple second fitting results. The processor is further configured to perform goodness-of-fit analysis on the insulation layer damage characteristics and each simulated insulation layer damage characteristic respectively, to determine multiple third fitting results. And based on the multiple first fitting results, the multiple second fitting results, and the multiple third fitting results, a target simulation model is determined from the insulation coupling model and the multiple conduction coupling models.

[0137] Specifically, the second volt-ampere characteristic relationship refers to the curve showing the relationship between the arc voltage and time obtained through actual measurement in the arc test. It is the dynamic electrical characteristic data in the experimental results, reflecting the changes in resistance and power throughout the entire process of arc initiation, development and extinction.

[0138] Conductor ablation characteristics refer to the characteristic parameters of physical damage such as melting, vaporization, and splashing that occur on the surface of a conductor under the action of an electric arc. These parameters include ablation location, ablation range, ablation depth, and ablation morphology, and serve as the basis for evaluating the thermal effect of an electric arc.

[0139] Insulation layer damage characteristics refer to the characteristic parameters of physicochemical damage such as pyrolysis, carbonization, cracking, and breakdown that occur in the insulation layer under the action of electric arc. These parameters include the extent of damage, degree of carbonization, thickness of carbonized layer, and crack distribution. They are key indicators for assessing the degradation behavior of insulation layers.

[0140] In some implementations, the second current-voltage characteristic relationship, conductor ablation characteristics, and insulation layer damage characteristics can be determined through the following steps: The experimental sample is placed in a preset experimental environment to simulate the surrounding environment when a superconducting magnet actually malfunctions, ensuring that the plasma characteristics and heat exchange process of the arc are consistent with actual operating conditions. A preset DC current is applied to the first and second conductors, and the initial arc is precisely triggered using a pre-embedded arc triggering element, initiating the ablation process of the insulation layer between the conductors.

[0141] Subsequently, voltage and current signals are simultaneously acquired during the ablation of the insulation layer between conductors to generate an volt-ampere characteristic curve for the entire arc development process. This volt-ampere characteristic curve allows for the calculation of parameters such as instantaneous power, resistance, and energy of the arc, enabling analysis of its dynamic changes. In some implementations, the volt-ampere characteristic curve plotting process can be as follows: The acquired voltage and current signals are filtered to remove power supply noise and electromagnetic interference. The signals are then divided into the arc initiation stage, stable combustion stage, and extinction stage according to the time axis. Simultaneously, the average voltage, average current, average power, and total energy for each stage are calculated. The volt-ampere characteristic curve for the entire arc development process is plotted with current as the x-axis and voltage as the y-axis.

[0142] Then, after the ablation of the experimental sample is completed, the conductor ablation characteristics and insulation layer damage characteristics are quantitatively observed and analyzed using equipment such as optical microscopes, scanning electron microscopes, and 3D profilometers to determine the conductor ablation characteristics and insulation layer damage characteristics of the experimental sample. In some embodiments, the observation and analysis of the conductor ablation characteristics and insulation layer damage characteristics of the experimental sample can be as follows: The sample after the experiment is photographed to record the overall ablation morphology. Then, a 3D profilometer is used to scan the conductor ablation area to obtain quantitative data on the ablation depth and ablation volume. Next, an optical microscope is used to observe the cross-section of the insulation layer, measuring the thickness and damage range of the carbide layer. Finally, the conductivity of the carbide layer is tested to assess the degree of degradation of the insulation layer.

[0143] The first fitting result refers to the quantitative fitting value calculated for the current-voltage characteristic dimension, which reflects the similarity between the simulated current-voltage characteristic curve and the experimental current-voltage characteristic curve.

[0144] The second fitting result refers to the quantitative fitting degree value calculated for the conductor ablation feature dimension, reflecting the similarity between the simulated conductor ablation feature and the experimental conductor ablation feature.

[0145] The third fitting result refers to the quantitative fitting value calculated for the dimension of insulation layer damage characteristics, reflecting the similarity between the simulated insulation layer damage characteristics and the experimental insulation layer damage characteristics.

[0146] In some implementations, the goodness-of-fit analysis of the second volt-ampere characteristic relationship and each first volt-ampere characteristic relationship can be performed using a calculation method combining Pearson correlation coefficient and root mean square error. First, the simulated voltage curve and the experimental voltage curve are time-aligned. Then, the Pearson correlation coefficient between the two curves is calculated, along with the root mean square error. Subsequently, multiple first fitting results are determined based on the Pearson correlation coefficient and root mean square error of the two curves.

[0147] The goodness-of-fit analysis of conductor ablation characteristics and each simulated conductor ablation characteristic can be performed using a multi-parameter weighted average calculation method. For example, the three most representative parameters—ablation length, maximum ablation depth, and average ablation depth—can be selected, and the relative error of each type of parameter can be calculated separately. Subsequently, weights are assigned to each type of parameter according to their importance, and multiple second-fit results are determined.

[0148] The fitting analysis of the insulation layer damage characteristics and each simulated insulation layer damage characteristic can be performed using a calculation method similar to that used for conductor ablation characteristics. For example, three parameters can be selected: carbonization area, maximum carbonization depth, and pyrolysis range. The relative errors can be calculated separately and then weighted to obtain multiple third fitting results.

[0149] After obtaining multiple first, second, and third fitting results, a target simulation model can be determined from the insulating coupling model and multiple conductive coupling models through multi-dimensional weighted fusion. Specifically, the first, second, and third fitting results are weighted and fused to obtain the overall fit, and the target simulation model is determined from the insulating coupling model and multiple conductive coupling models based on this overall fit.

[0150] Thus, goodness-of-fit analyses were performed on the second volt-ampere characteristic relationship and each first volt-ampere characteristic relationship to determine multiple first fitting results. Next, goodness-of-fit analyses were performed on the conductor ablation characteristics and each simulated conductor ablation characteristic to determine multiple second fitting results. Then, goodness-of-fit analyses were performed on the insulation layer damage characteristics and each simulated insulation layer damage characteristic to determine multiple third fitting results. Finally, based on the multiple first fitting results, multiple second fitting results, and multiple third fitting results, a self-insulation coupling model and multiple conduction coupling models were used to determine the target simulation model. In this way, through multi-dimensional goodness-of-fit analyses of the volt-ampere characteristic relationship, ablation characteristics, and damage characteristics, it can be ensured that the target simulation model highly matches the experimental results in both the volt-ampere characteristic relationship and ablation characteristics, thereby enabling the selected target simulation model to reflect the conductive behavior of the arc and the inter-turn insulation layer of the superconducting magnet.

[0151] Please see Figure 8 In some implementations, step 05 includes: 051: Based on the conductivity sub-model corresponding to the target simulation model, the conductivity characteristics of the inter-turn insulation layer under the action of the initial electric arc are determined in order to analyze the influence of the degradation of insulation conductivity characteristics on the arc behavior.

[0152] In some implementations, the processor is also used to determine the conductivity characteristics of the inter-turn insulation layer under the action of the initial electric arc based on the conductivity sub-model corresponding to the target simulation model, so as to analyze the impact of the degradation of insulation conductivity characteristics on the arc behavior.

[0153] Specifically, the conductivity characteristics under the action of the initial electric arc refer to the dynamic characteristics of the inter-turn insulation layer as it gradually transforms from an initial high insulation state to a conductive state through pyrolysis, semi-carbonization, and complete carbonization under the transient high temperature generated by the initial electric arc. This includes key parameters such as conductivity values ​​at different temperatures, the starting temperature of the conductivity transformation, the transformation rate, and the saturation conductivity.

[0154] The degradation of insulation and conductivity properties refers to the irreversible process by which insulating materials, under the influence of electric arc heat, undergo physicochemical changes such as molecular chain breakage, pyrolysis, and carbonization, resulting in a decrease in insulation performance and an increase in conductivity. The degree of degradation mainly depends on the temperature and duration of the electric arc, as well as the thermal stability of the insulating material.

[0155] Arc behavior refers to the various characteristics exhibited by an electric arc throughout its entire development process, from its initiation to its extinction. These characteristics include the arc ignition voltage, ignition time, stable combustion voltage, combustion duration, propagation speed, propagation direction, and extinction conditions. Arc behavior directly determines the severity of short-circuit faults and the degree of damage to superconducting magnets.

[0156] Based on the conductivity sub-model corresponding to the target simulation model that has been validated in multiple dimensions, the evolution law of dynamic conductivity characteristics of the inter-turn insulation layer under the action of initial electric arc is first quantitatively determined. Then, based on this evolution law of dynamic conductivity characteristics, the influence mechanism of insulation conductivity degradation on key behaviors such as arc initiation, stable combustion, propagation path and extinction is analyzed in depth. Finally, a quantitative relationship between insulation conductivity characteristics and arc fault risk is established, providing a direct basis for the safe design, insulation selection and protection strategy formulation of superconducting magnets.

[0157] Thus, based on the conductivity sub-model corresponding to the target simulation model, the conductivity characteristics of the inter-turn insulation layer under the initial arc are determined to analyze the impact of insulation conductivity degradation on arc behavior. This allows for a quantitative assessment of the actual impact of insulation conductivity degradation on arc behavior, providing a foundation for short-circuit arc risk assessment in superconducting magnets.

[0158] This application also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, it performs the steps of the method described above.

[0159] It is understood that a computer program includes computer program code. Computer program code can be in the form of source code, object code, executable files, or some intermediate form. Computer-readable storage media can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), and software distribution media, etc.

[0160] This application also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the above-described method.

[0161] In this specification, the terms "specifically," "furthermore," "particularly," "understandably," etc., refer to specific features, structures, materials, or characteristics described in connection with embodiments or examples that are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0162] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of executable request code comprising one or more steps for implementing a particular logical function or process, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order according to the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0163] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application.

Claims

1. A method for evaluating the conductivity behavior of the inter-turn insulation layer of a superconducting magnet during short-circuit arc propagation, characterized in that, The method includes: A benchmark simulation structure with the same geometry as the experimental sample is constructed. The experimental sample is matched with the superconducting magnet to be evaluated. The experimental sample is used for the arc test of the inter-turn insulation layer of the superconducting magnet. The benchmark simulation structure is provided with an arc channel at the simulated arc trigger position. The simulated arc trigger position corresponds to the preset arc trigger position of the experimental sample. The arc channel is used to simulate the initial arc. For the simulated insulating element in the benchmark simulation structure that corresponds to the conductor insulation layer of the experimental sample, multiple different conductivity sub-models are configured to obtain multiple experimental simulation models with different conductivity characteristics. Each experimental simulation model corresponds to one conductivity sub-model, and the conductivity sub-model is used to indicate the conductivity characteristics of the simulated insulating element in the experimental simulation model. A preset DC current consistent with the electric arc test is applied to multiple experimental simulation models respectively, and multiple simulation results are determined, wherein each simulation result corresponds to one of the experimental simulation models; The goodness-of-fit analysis is performed on multiple simulation results and experimental results, and the target simulation model with the highest goodness of fit with the experimental sample is selected from multiple experimental simulation models, wherein the experimental results are obtained based on the electric arc test; The conductivity behavior of the inter-turn insulation layer is evaluated based on the conductivity sub-model corresponding to the target simulation model.

2. The method according to claim 1, characterized in that, The experimental sample includes a first conductor, a second conductor, and an interconductor insulating layer arranged in parallel with each other. Wherein, the cross-sectional dimensions of the first conductor are consistent with the cross-sectional dimensions of the conductor used in the superconducting magnet, and the cross-sectional dimensions of the second conductor are consistent with the cross-sectional dimensions of the conductor used in the superconducting magnet; The first insulation structure of the inter-conductor insulation layer is consistent with the second insulation structure of the inter-turn insulation layer, and an arc triggering element is embedded at the preset arc triggering position in the inter-conductor insulation layer.

3. The method according to claim 1, characterized in that, The arc channel includes a plasma region, which adjusts the electric field strength and power characteristics of the initial arc through an equivalent thermal conductivity or a thermal conductivity scaling factor β.

4. The method according to claim 3, characterized in that, The plasma region achieves the equivalent of the electric arc propagation process in the following way: Ignoring the radiation source term S in the arc heat conduction control equation, and introducing the thermal conductivity scaling factor β into the thermal conductivity term, we obtain the equivalent heat conduction control equation. The governing equation for arc heat conduction is: (1) The equivalent heat conduction control equation is: (2) Where ρ is the material density of the plasma, Cp is the specific heat capacity of the plasma at constant pressure, T is the current instantaneous temperature, t is time, r is the radial spatial coordinate, K is the original thermal conductivity of the plasma, σ is the electrical conductivity of the plasma, E is the electric field strength of the plasma, and S is the radiation source term.

5. The method according to claim 4, characterized in that, The thermal conductivity scaling factor β is a non-fixed value and is adjusted during the simulation based on the experimental results of the electric arc test; the adjustment process includes: According to the different stages of the arc development process, a corresponding initial value of β is set for each stage. Numerical simulations were performed based on different β values ​​to obtain the corresponding simulation results; The simulation results are compared with the experimental results to determine the goodness of fit. When the simulation results and the experimental results meet the preset consistency conditions, the corresponding β parameter value is determined.

6. The method according to claim 5, characterized in that, The different stages of the arc development process include a first stage in which the arc moves within the inter-turn insulation, and a second stage in which the arc length increases after the conductor melts; the first stage and the second stage correspond to different β parameter values, and the β parameter value of the second stage is greater than the β parameter value of the first stage.

7. The method according to claim 1, characterized in that, The conductivity sub-model includes a first type of sub-model and a second type of sub-model. The first type of sub-model is used to indicate that the simulated insulating element is a non-conductive element, and the second type of sub-model is used to indicate that the simulated insulating element is a conductive element. Each second type of sub-model corresponds to a set of independent conductivity sub-model parameters.

8. The method according to claim 7, characterized in that, Each set of conductivity sub-model parameters includes the minimum conductivity of the simulated insulating element, the maximum conductivity of the simulated insulating element, the reference temperature at which the simulated insulating element is at the minimum conductivity, the transition temperature at which the conductivity of the simulated insulating element changes, and the temperature difference between the minimum conductivity and the maximum conductivity of the simulated insulating element.

9. The method according to claim 8, characterized in that, The second type of sub-model is determined by the following relation: ； in, The current instantaneous temperature of the simulated insulating element. The current instantaneous conductivity of the simulated insulating element at its current instantaneous temperature T. The minimum conductivity, The maximum conductivity is... The Gaussian error function is... The reference temperature is... The transition temperature is... This refers to the transition temperature difference.

10. The method according to claim 7, characterized in that, The experimental simulation model includes an insulation coupling model and a conductivity coupling model. For the simulated insulating element in the benchmark simulation structure corresponding to the inter-conductor insulation layer of the experimental sample, multiple different conductivity sub-models are configured to obtain multiple experimental simulation models with different conductivity characteristics, including: The first type of sub-model is set for the simulated insulating element in the benchmark simulation structure to generate the insulation coupling model; Multiple second-type sub-models with different conductivity sub-model parameters are set for the simulated insulating element in the benchmark simulation structure to generate multiple conductive coupling models, wherein each conductive coupling model corresponds to one of the second-type sub-models.

11. The method according to claim 10, characterized in that, The process involves applying a preset DC current, consistent with the electric arc test, to multiple experimental simulation models to determine multiple simulation results, including: The preset DC current is applied to the insulation coupling model and multiple conductive coupling models respectively to simulate and determine multiple simulation results. The preset DC current is a constant current. Each simulation result includes a first volt-ampere characteristic relationship, simulated conductor ablation characteristics, and simulated insulation layer damage characteristics.

12. The method according to claim 11, characterized in that, The experimental results include the second volt-ampere characteristic relationship, conductor ablation characteristics, and insulation layer damage characteristics. The fitting analysis of multiple simulation results and experimental results is performed to select the target simulation model with the highest fitting degree to the experimental sample from multiple experimental simulation models, including: A goodness-of-fit analysis was performed on the second current-voltage characteristic relationship and each of the first current-voltage characteristic relationships to determine multiple first fitting results; A goodness-of-fit analysis was performed on the conductor ablation characteristics and each of the simulated conductor ablation characteristics to determine multiple second fitting results; A goodness-of-fit analysis was performed on the insulation layer damage characteristics and each simulated insulation layer damage characteristic to determine multiple third-fit results; Based on multiple first fitting results, multiple second fitting results, and multiple third fitting results, the target simulation model is determined from the insulating coupling model and multiple conductive coupling models.

13. The method according to claim 1, characterized in that, The step of evaluating the conductivity behavior of the inter-turn insulation layer based on the conductivity sub-model corresponding to the target simulation model includes: Based on the conductivity sub-model corresponding to the target simulation model, the conductivity characteristics of the inter-turn insulation layer under the action of the initial electric arc are determined in order to analyze the influence of insulation conductivity degradation on arc behavior.

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