High-temperature superconducting cable equivalent analysis method and system, medium and electronic equipment

Abstract

The invention discloses a high-temperature superconducting cable equivalent analysis method, a high-temperature superconducting cable equivalent analysis system, a medium and electronic equipment, and relates to the technical field of power devices and superconducting power transmission. Constructing a first equivalent circuit model based on the structural characteristic parameter set, and performing cross generality screening on the material parameters by adopting a multi-factor influence separation method to obtain a first equivalent parameter set; constructing a first coupling model based on the first equivalent parameter set, and applying disturbance signals of different frequencies to perform fault simulation to obtain a working condition equivalent model; extracting transient response data based on the working condition equivalent model, and identifying transient quenching response characteristics of the high-temperature superconducting cable based on the transient response data; according to the method, a multi-objective optimization function is constructed based on transient quench response characteristics, control parameters are optimized by adopting an NSGA-III algorithm, an optimal control strategy is obtained, and the problems of high quench expansion risk and difficulty in timely regulation and control of the high-temperature superconducting cable under a transient fault are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power devices and superconducting power transmission, and more particularly, relates to a high-temperature superconducting cable equivalent analysis method, system, medium and electronic device. BACKGROUND

[0002] High-temperature superconducting cables have high application potential in urban power grid upgrading, high-capacity power transmission, and high-reliability power system construction due to their low energy loss, high current density, strong electromagnetic compatibility, and compact and lightweight structural characteristics. Compared with traditional copper and aluminum conductor cables, superconducting cables can transmit larger currents in smaller volumes, significantly reducing power transmission loss and energy consumption, providing a feasible approach to energy-saving and efficient power transmission. In addition, its low electromagnetic radiation and excellent anti-interference performance also make it have unique advantages in urban centers, data centers, high-speed rail transportation, and other places with strict requirements on power quality.

[0003] However, during operation, especially when encountering transient faults such as short circuits, overloads, or partial faults, the superconducting layer of the high-temperature superconducting cable may quickly lose superconductivity, forming a local or locally expanding quench region. Due to the high current density and high energy density of the high-temperature superconducting cable, the quench region will rapidly expand, causing a sudden increase in resistance, local heating, and rapid energy release, thereby posing a serious threat to the safe operation of the cable. At the same time, traditional monitoring and control methods often cannot accurately identify the quench starting position, propagation speed, and influence range in the millisecond-level transient process, making it difficult for the refrigeration system and protection measures to respond in time and effectively suppress quench propagation. This not only may cause local damage to the cable, but also may affect the stability and reliability of the entire power system.

[0004] To solve the above problems, the present application provides a solution. SUMMARY

[0005] To overcome the above-mentioned defects of the prior art, embodiments of the present application provide a high-temperature superconducting cable equivalent analysis method, system, medium and electronic device, which establishes an equivalent model of the high-temperature superconducting cable and analyzes its transient quench response to solve the problem of high quench expansion risk and difficulty in timely regulation and control of the high-temperature superconducting cable under transient faults.

[0006] To achieve the above-mentioned purposes, the present application provides the following technical solutions: The application discloses a high-temperature superconducting cable equivalent analysis method, which comprises the following steps: collecting a structural characteristic parameter set of a high-temperature superconducting cable, and constructing a first equivalent circuit model based on the structural characteristic parameter set; based on the first equivalent circuit model, adopting a multi-factor influence separation method to cross-commonly screen material parameters to obtain a first equivalent parameter set; constructing a first coupling model based on the first equivalent parameter set, and applying disturbance signals of different frequencies to the first coupling model to perform fault simulation to obtain a working condition equivalent model; extracting transient response data based on the working condition equivalent model, and identifying transient quench response characteristics of the high-temperature superconducting cable based on the transient response data; constructing a multi-objective optimization function based on the transient quench response characteristics, and optimizing control parameters by adopting an NSGA-III algorithm to obtain an optimal control strategy.

[0007] In a preferred embodiment, the collecting a structural characteristic parameter set of a high-temperature superconducting cable, and constructing a first equivalent circuit model based on the structural characteristic parameter set, specifically comprises: analyzing geometric dimensions and material characteristic parameters of the high-temperature superconducting cable to obtain a copper framework diameter, a superconducting tape layer number, a width, a thickness, a winding angle and a material resistivity temperature characteristic; calculating a copper framework resistance based on the copper framework diameter and the material resistivity temperature characteristic; calculating an equivalent resistance and an equivalent inductance of each layer of superconducting tape according to the superconducting tape layer number, the width, the thickness and the winding angle; obtaining a spatial position relationship of each layer of conductor, and calculating interlayer mutual inductance parameters based on the spatial position relationship; obtaining an outer diameter of a shielding layer and a relative dielectric constant and calculating interlayer distributed capacitance; and integrating the copper framework resistance, the equivalent resistance and the equivalent inductance, the interlayer mutual inductance parameters and the interlayer distributed capacitance to construct the first equivalent circuit model.

[0008] In a preferred embodiment, the based on the first equivalent circuit model, adopting a multi-factor influence separation method to cross-commonly screen material parameters to obtain a first equivalent parameter set, specifically comprises: extracting multi-dimensional influence factors of material parameters from the first equivalent circuit model to construct a multi-factor influence separation matrix, wherein the multi-dimensional influence factors comprise temperature variation characteristics, current load rates and frequency response characteristics; based on the multi-factor influence separation matrix, mapping the multi-dimensional influence factors of each material parameter to an orthogonal characteristic space to obtain mapped multi-dimensional influence factors; and adopting a cross-commonly screening algorithm to linearly evaluate the mapped multi-dimensional influence factors, and screening material parameters according to an evaluation result to obtain the first equivalent parameter set.

[0009] In a preferred embodiment, the first coupling model is constructed based on the first equivalent parameter set, and a fault simulation is performed on the first coupling model by applying disturbance signals of different frequencies to obtain a working condition equivalent model, specifically: mapping the first equivalent parameter set into electromagnetic fields, thermal fields and stress fields to establish field coupling equations; discretizing the field coupling equations to obtain discretized field coupling equations and solving the discretized field coupling equations by using a finite element method to obtain the first coupling model; applying sweep-frequency disturbance signals from low frequencies to high frequencies to the first coupling model and obtaining dynamic response data of the first coupling model under each sweep-frequency disturbance signal; analyzing the dynamic response data, extracting a fault feature mode, and correcting parameters of the first coupling model based on the feature mode to obtain the working condition equivalent model.

[0010] In a preferred embodiment, transient response data is extracted based on the working condition equivalent model, and a transient quench response characteristic of the high-temperature superconducting cable is identified based on the transient response data, specifically: constructing a transient response time series by applying a pulse current signal to the working condition equivalent model; performing empirical mode decomposition on the transient response time series, extracting intrinsic mode function components, and calculating the Hilbert spectrum of the intrinsic mode function components to obtain a time-frequency energy distribution matrix; identifying a quench triggering time and a quench propagation path from the time-frequency energy distribution matrix; and based on the quench triggering time and the propagation path, drawing a transient quench response characteristic curve, wherein the transient quench response characteristic curve includes a quench front speed and a recovery time.

[0011] In a preferred embodiment, the transient response time series is subjected to empirical mode decomposition to extract intrinsic mode function components, specifically: identifying all extreme points of the transient response time series and constructing upper and lower envelope lines; calculating the mean of the upper and lower envelope lines and calculating the residual of the transient response time series and the mean; repeating the above process until the residual meets a preset intrinsic mode function condition to obtain a first intrinsic mode function component; subtracting the first intrinsic mode function component from the transient response time series to obtain a residual sequence and continuing to decompose the residual sequence until the residual sequence is a monotonic function.

[0012] In a preferred embodiment, a multi-objective optimization function is constructed based on the transient quench response characteristic, and a NSGA-III algorithm is used to optimize the control parameters to obtain an optimal control strategy, specifically: defining a multi-objective optimization function based on the transient quench response characteristic, wherein the multi-objective optimization function includes minimizing quench response time, minimizing peak temperature and maximizing system stability; initializing a control parameter population and setting a parameter range; performing multi-objective optimization using the NSGA-III algorithm, generating new individuals by simulated crossover and mutation in each generation, and calculating the multi-objective optimization function value of each new individual; calculating the non-dominated level and crowding distance of each new individual based on the multi-objective optimization function value, and selecting the optimal control strategy based on the non-dominated level and crowding distance.

[0013] The technical effects and advantages of the high-temperature superconducting cable equivalent analysis method, system, medium and electronic equipment of the present application are as follows: The present application realizes accurate modeling and rapid prediction of high-temperature superconducting cables under transient fault conditions by constructing an equivalent analysis model of multi-physical coupling of electromagnetic field, thermal field and stress field, and combining the dynamic response characteristics of the swept frequency disturbance signal and the multi-objective optimization strategy. Compared with traditional static or single-field simulation methods, the present application can capture key features such as current redistribution, temperature surge and stress concentration in real time when the cable loses superconductivity locally, and then identify the superconductivity loss trigger position and propagation path, thereby fundamentally revealing the mechanism of superconductivity loss expansion. At the same time, through the joint application of empirical mode decomposition and NSGA-III multi-objective optimization algorithm, the system can automatically correct the equivalent model parameters and optimize the cooling and protection strategy, realize the coordinated control of superconductivity loss response time, peak temperature and system stability, significantly reduce the superconductivity loss expansion risk of high-temperature superconducting cables under transient faults, and improve the safety margin and operation reliability of the system, providing a high-precision and generalizable technical means for dynamic safety evaluation and intelligent control of high-temperature superconducting power transmission projects. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 The present application is a flowchart of a high-temperature superconducting cable equivalent analysis method.

[0015] Figure 2 The present application is a structural diagram of a high-temperature superconducting cable equivalent analysis system.

[0016] Figure 3 The present application is a structural diagram of an electronic device for a high-temperature superconducting cable equivalent analysis method. DETAILED DESCRIPTION

[0017] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0018] Embodiment 1, Figure 1 The present application is a high-temperature superconducting cable equivalent analysis method, comprising the following steps: S1, obtaining the actual structure parameters of the high-temperature superconducting cable, and constructing a first equivalent circuit model based on the actual structure parameters; In this example, the structural characteristic parameter set of the high-temperature superconducting cable is collected, and a first equivalent circuit model is constructed based on the structural characteristic parameter set, specifically: The geometric size and material characteristic parameters of the high-temperature superconducting cable are analyzed to obtain the copper framework diameter, the superconducting tape layer number, the width, the thickness, the winding angle and the material resistivity temperature characteristic; Based on the copper framework diameter and the material resistivity temperature characteristic, the copper framework resistance is calculated. According to the superconducting tape layer number, the width, the thickness and the winding angle, the equivalent resistance and the equivalent inductance of each layer of superconducting tape are calculated. The spatial position relationship of each layer of conductors is obtained, and the interlayer mutual inductance parameters are calculated based on the spatial position relationship. The shielding layer outer diameter and the relative dielectric constant are obtained, and the interlayer distributed capacitance is calculated. The copper framework resistance, the equivalent resistance and the equivalent inductance, the interlayer mutual inductance parameters and the interlayer distributed capacitance are integrated to construct a first equivalent circuit model.

[0019] In this example, the calculation formula of the equivalent resistance and the equivalent inductance of each layer of superconducting tape is as follows: The calculation formula of the equivalent resistance is as follows:

[0020] Wherein, is the equivalent resistance of the copper stabilizing layer and the YBCO layer in the i-th layer of superconducting tape, is the density of the copper stabilizing layer and the YBCO layer in the i-th layer of superconducting tape, is the number of parallel tapes, , and are the width, the length and the thickness of the superconducting tape respectively, is the winding angle of the i-th layer of superconducting tape.

[0021] The calculation formula of the equivalent inductance is as follows:

[0022] Wherein, is the equivalent inductance of the i-th layer of superconducting tape, is the vacuum permeability, is the shielding layer outer diameter, is the outer radius of the i-th layer of superconducting tape.

[0023] In this example, the calculation formula of the interlayer distributed capacitance is as follows:

[0024] Wherein, is the interlayer distributed capacitance, is the relative dielectric constant of the shielding material, is the vacuum dielectric constant, is the outer radius of the j-th layer of superconducting tape.

[0025] It should be noted that first, the high-temperature superconducting cable is structurally analyzed to obtain geometric size and material characteristic parameters. For example, it is assumed that the cable length is 100 m, the copper skeleton diameter is 10 mm, the superconducting tape is divided into three layers, the tape width of each layer is 4 mm, the thickness is 0.2 mm, and the winding angle is 30°, 45° and 60° respectively. At the same time, the characteristics of the material resistivity changing with temperature are obtained, for example, the resistivity of the copper skeleton is 0.2 μΩ·cm at 77 K and 1.7 μΩ·cm at 295 K. Through these data, the geometric structure parameter set and the material characteristic parameter set of the cable can be obtained, providing a basis for subsequent equivalent circuit model calculation.

[0026] Further, the copper skeleton diameter and the resistivity temperature characteristics are used for resistance calculation. For example, the copper skeleton diameter is 10 mm, corresponding to a cross-sectional area of about 78.5 mm². Combined with the material resistivity of 0.2 μΩ·cm at 77 K, it is converted into the resistance value under the corresponding length, for example, the resistance of the 100 m long copper skeleton is about 0.025 Ω. This resistance value will be used as the copper skeleton resistance parameter in the first equivalent circuit model, to reflect the conductive characteristics of the copper skeleton under different temperature and current conditions.

[0027] In addition, first, the actual winding position of each layer of superconducting tape in the cable is obtained. For example, the first layer of tape is close to the copper skeleton, the second layer is offset by 2 mm outside the first layer, and the third layer is offset by 2 mm outside the second layer, and the winding angle of each layer is 30°, 45° and 60° respectively. According to these spatial position relationships, the mutual inductance parameters between each layer of conductors can be calculated. For example, the mutual inductance between the first layer and the second layer is 0.15 μH / m, and the mutual inductance between the second layer and the third layer is 0.12 μH / m. The mutual inductance parameters obtained in this way can truly reflect the electromagnetic coupling characteristics between the conductors of each layer, providing a basis for constructing the coupled equivalent circuit.

[0028] Finally, the copper skeleton resistance, the equivalent resistance of each layer of superconducting tape, the equivalent inductance, the interlayer mutual inductance parameters obtained in Example 3, and the distribution capacitance between each layer are integrated to construct the first equivalent circuit model of the high-temperature superconducting cable. For example, the copper skeleton resistance is 0.025 Ω, the first layer of superconducting tape equivalent resistance is 0.01 Ω, the inductance is 0.2 μH / m, the interlayer mutual inductance parameters are 0.15 μH / m and 0.12 μH / m respectively, and the interlayer distribution capacitance is 0.05 μF / m. These parameters are connected in network according to the hierarchical structure of the cable in the simulation software, and the complete first equivalent circuit model can be obtained, which can be used for subsequent material parameter nonlinear correction and transient simulation analysis.

[0029] S2, based on the first equivalent circuit model, using a multi-factor influence separation method to cross common screening of material parameters, obtaining a first equivalent parameter set; In the present example, based on the first equivalent circuit model, a multi-factor influence separation method is used to cross-commonly screen the material parameters to obtain a first equivalent parameter set, specifically: Multi-dimensional influence factors of the material parameters are extracted from the first equivalent circuit model, and a multi-factor influence separation matrix is constructed, the multi-dimensional influence factors including temperature variation characteristics, current load rate, and frequency response characteristics; Based on the multi-factor influence separation matrix, the multi-dimensional influence factors of each material parameter are mapped to an orthogonal characteristic space to obtain the mapped multi-dimensional influence factors. The cross-commonly screening algorithm is used to linearly evaluate the mapped multi-dimensional influence factors, and the material parameters are screened according to the evaluation results to obtain the first equivalent parameter set.

[0030] It should be noted that, first, based on the first equivalent circuit model constructed as described above, multi-dimensional influence factors of each material parameter in the high-temperature superconducting cable are extracted. Specifically, representative material parameters are selected, such as the critical current density of the superconducting tape, the resistivity of the copper skeleton, the dielectric constant of the insulation layer, and the magnetic flux pinning strength of the superconducting tape. For each material parameter, controlled perturbation is introduced in the model, and the response change of the model under different external conditions is observed to identify its influence characteristics in three main dimensions: temperature variation characteristics, current load rate characteristics, and frequency response characteristics.

[0031] Exemplarily, taking a typical three-layer high-temperature superconducting cable as an example, the temperature is segmented to increase from 30K to 90K, the nonlinear change trend of the output voltage of the model is recorded to form a temperature variation characteristic curve, which reflects the sensitivity of the material parameters to temperature change. Taking the rated current as a reference, the current load rate is gradually increased to 150%, and the current distribution and electromagnetic loss change rate are recorded to construct the current load rate characteristics. Finally, by applying a sweep frequency signal of 50Hz to 5kHz, the system impedance and phase difference change curve are obtained to establish the frequency response characteristics. After standardizing the above three types of characteristic data, they are arranged into a multi-factor influence separation matrix with material parameters as rows and influence factors as columns. This matrix directly reflects the contribution of different material parameters to the electromagnetic response of the overall model under multi-dimensional environment, providing a basis for subsequent orthogonal mapping.

[0032] Secondly, after obtaining the multi-factor influence separation matrix, in order to eliminate the coupling and redundancy between different dimensions, the principal characteristic decoupling method is used to map each influence factor to the orthogonal characteristic space. The specific process is as follows: first, the change trend of each influence factor in the matrix is centralized to make its mean value zero; then, the change trend of each material parameter under three-dimensional characteristics is analyzed for independence, and the interrelated parts of temperature change characteristics, current load rate characteristics and frequency response characteristics are stripped. Taking the copper skeleton resistivity as an example, this parameter has a significant impact when the temperature rises, but the impact is weak under high frequency disturbance; while the critical current density of superconducting tape shows strong nonlinear coupling relationship under temperature and frequency change. Through orthogonal mapping, the temperature dominant type and coupling dominant type characteristics are projected onto independent coordinate axes respectively, so that each material parameter in the new orthogonal space is represented by a set of independent characteristic vectors. After mapping, the copper skeleton resistivity mainly shows a single direction high weight characteristic, while the critical current density of superconducting tape has significant components in two orthogonal directions, thereby realizing independent expression of material influence characteristics.

[0033] Further, after completing the orthogonal mapping, the embodiment further adopts a cross commonness screening algorithm to linearly evaluate the multi-dimensional influence factors of material parameters. The core idea of the algorithm is to identify key parameters that show consistent influence trends under different working conditions, while eliminating parameters driven by chance or noise.

[0034] For example, under five different external environmental conditions (including low temperature steady state, high frequency disturbance, overload operation, rapid cooling and partial quenching state), the characteristic vector response of each material parameter in the orthogonal space is extracted respectively, and the trend similarity between them is calculated. If the characteristic vector of a parameter (such as copper skeleton resistivity) shows linear change in the same direction under five working conditions, it means that the parameter has common influence on the system response and is classified into the high weight category; if the characteristic vector of another parameter (such as the dielectric constant of the insulation layer) changes in different directions under different working conditions, it is determined as a non-common factor and is down-weighted. Through this process, unstable or low sensitivity material parameters can be effectively filtered out, and only the parameters that have a lasting contribution to the equivalent behavior of the cable are retained.

[0035] Finally, after obtaining the linear evaluation results, the embodiment determines the final first equivalent parameter set according to the parameter weight ranking. The screening criterion is: only parameters with a commonality influence degree exceeding a set threshold (such as 0.75) under all working conditions are retained. Taking the actual analysis results as an example, among the 12 candidate material parameters, the critical current density of the superconducting tape, the copper skeleton resistivity, the interlayer mutual inductance coefficient, the contact interface thermal resistance and the superconducting tape magnetic flux pinning strength are identified as high-weight parameters, and their comprehensive contribution degree exceeds 85%. These parameters are included in the first equivalent parameter set, which is used for subsequent coupling model construction and dynamic simulation; while other parameters such as the relative dielectric constant of the insulating layer or the thickness of the shielding layer are excluded due to lower commonality influence. The final first equivalent parameter set can accurately represent the main electromagnetic response characteristics of the high-temperature superconducting cable with fewer parameter dimensions, thereby significantly improving the model calculation efficiency and stability.

[0036] S3, constructing a first coupling model based on the first equivalent parameter set, and applying disturbance signals of different frequencies to the first coupling model for fault simulation to obtain a working condition equivalent model; In this example, a first coupling model is constructed based on the first equivalent parameter set, and disturbance signals of different frequencies are applied to the first coupling model for fault simulation to obtain a working condition equivalent model, specifically: mapping the first equivalent parameter set to electromagnetic fields, thermal fields and stress fields to establish field coupling equations; discretizing the field coupling equations to obtain discretized field coupling equations and solving the discretized field coupling equations by using a finite element method to obtain the first coupling model; applying sweep disturbance signals from low frequency to high frequency to the first coupling model, and obtaining dynamic response data of the first coupling model under each sweep disturbance signal; analyzing the dynamic response data, extracting a fault feature mode, and correcting the parameters of the first coupling model based on the feature mode to obtain a working condition equivalent model.

[0037] It should be noted that first, the first equivalent parameter set is introduced into the multi-physical field simulation environment to realize the coupled modeling of electromagnetic field, thermal field and stress field. Specifically, according to the structural characteristics and material properties of the high temperature superconducting cable, the physical meaning of each parameter is respectively mapped to different field domains. For example, the critical current density and the magnetic flux pinning strength of the superconducting tape are mapped to the electromagnetic field module to represent the current distribution and the magnetic flux motion characteristics; the copper skeleton resistivity and the interlayer mutual inductance coefficient are mapped to the electromagnetic-thermal field interaction interface to describe the joule loss and the local temperature rise caused by the magnetic field change; in addition, the contact interface thermal resistance and the tape thermal conductivity are included in the thermal field module to depict the heat diffusion and cooling efficiency; in addition, the mechanical strength and the thermal expansion coefficient of the superconducting tape are mapped to the stress field to reflect the thermal stress distribution caused by temperature gradient. Taking a high temperature superconducting cable with a rated current of 3kA and a working temperature of 77K as an example, a three-dimensional geometric model is established through the COMSOL Multiphysics platform, and the above equivalent parameters are assigned to the corresponding subdomains and boundary conditions. The electromagnetic field equation is used to solve the current density and magnetic flux density distribution, the thermal field equation is used to solve the steady-state and transient temperature field, and the stress field equation is used to describe the strain distribution caused by thermal expansion and electromagnetic force. The three fields interact through the shared parameter boundary, thereby forming a field coupling equation set to provide a basis for subsequent finite element solution.

[0038] Secondly, after establishing the complete multi-field coupling equation, the finite element method is used to discretize and solve the equation to obtain the first coupling model. Specifically, by dividing the cable geometric model into refined tetrahedral mesh elements, the electromagnetic, thermal and mechanical quantities within each element can be approximately linearly distributed, thereby converting the continuous field problem into a solution problem of discrete nodes. For the superconducting cable model with three-layer winding structure, about 1.2×10 6 finite element units are divided, in which the minimum size of the mesh in the superconducting tape area is set to 0.05mm to ensure accurate capture of the magnetic flux distribution and thermal flow gradient. During the calculation process, a multi-physical field iterative solution strategy is adopted: first, the steady-state distribution of the electromagnetic field is solved, and then the heat source term caused by electromagnetic loss is transferred to the thermal field module to calculate the temperature rise distribution; then the temperature field result is fed back to the stress field module to solve the deformation and stress concentration caused by thermal expansion and contraction, and finally the iterative convergence of the three fields is realized. The first coupling model obtained in this way can truly reflect the multi-field coupling characteristics of the cable under the given structure and material parameter conditions.

[0039] Furthermore, after obtaining the first coupling model, to study the response characteristics of the cable under different operating conditions, a frequency sweep perturbation signal from low to high frequency was applied to the model, and the corresponding dynamic response data was recorded. Specifically, an AC perturbation signal with an amplitude of 5% of the rated current was applied at the electromagnetic field input end, covering a frequency range of 10Hz to 10kHz, with each frequency step set to 100 Hz. Through frequency sweep simulation, the frequency response characteristics of the cable's internal magnetic field distribution, induced current density, and local temperature rise can be systematically analyzed. Taking a real sample as an example, when the frequency increased from 100 Hz to 2 kHz, the model showed an edge aggregation effect in the induced current distribution inside the superconducting tape, resulting in an increase of approximately 1.8 K in the surface temperature rise of the tape. When the frequency continued to rise to 8 kHz, the current transfer within the copper skeleton was significantly enhanced, and the stress amplitude in the local stress concentration area increased by approximately 12%. All response data were derived in time series form, including variables such as current density, magnetic flux change rate, temperature gradient, and stress fluctuation, providing a data foundation for subsequent fault characteristic analysis.

[0040] Finally, the dynamic response data is analyzed to extract fault characteristic patterns and correct model parameters based on these patterns, thus forming an equivalent operating condition model. Specifically, firstly, features are extracted from the time series of current, temperature, and stress at different frequencies, and abnormal peaks, hysteresis phases, or abrupt changes are identified through time-frequency analysis. For example, when the frequency is higher than 3kHz, the magnetic flux response of the superconducting layer shows a delay of about 1.2 ms, and the temperature response curve shows a nonlinear surge; this coupling anomaly is identified as a potential "precursor mode of quench failure." At a low frequency of 50Hz, the current distribution of the copper skeleton exhibits periodic asymmetry, corresponding to a "local heat accumulation mode." By statistically analyzing the occurrence patterns of these modes under multi-frequency operating conditions, a fault characteristic database is formed. Then, based on the feature matching results, key parameters in the original first coupling model (such as contact interface thermal resistance and the critical current density of the superconducting layer) are corrected to ensure that the model's response under specific operating conditions is consistent with experimental data or historical records. The corrected model is defined as the "equivalent operating condition model." Taking the sample in this embodiment as an example, the temperature rise prediction error of the corrected model under 77K conditions was reduced from the original 9.6% to 2.8%, and the stress distribution deviation was reduced to less than 5%, which significantly improved the model's fidelity and reliability to the actual operating conditions.

[0041] S4. Extract transient response data based on the equivalent model of the working condition, and identify the transient quench response characteristics of the high-temperature superconducting cable based on the transient response data. In this example, transient response data is extracted based on the operating condition equivalent model, and the transient quench response characteristics of the high-temperature superconducting cable are identified based on the transient response data. Specifically: A pulsed current signal is applied to the equivalent model of the working condition to construct a transient response time series; Empirical mode decomposition is performed on the transient response time series to extract the intrinsic mode function components and calculate the Hilbert spectrum of the intrinsic mode function components to obtain the time-frequency energy distribution matrix; Identify the quench trigger time and quench propagation path from the time-frequency energy distribution matrix; Based on the quench trigger time and propagation path, a transient quench response characteristic curve is plotted, which includes the quench leading edge velocity and recovery time.

[0042] It should be noted that, in order to study the dynamic characteristics of high-temperature superconducting cables under transient disturbance conditions, the aforementioned equivalent operating condition model was used as the analysis object, and a pulsed current signal was applied to excite the transient response. Specifically, the pulsed current signal was set to vary within 120% of the rated current amplitude, with a pulse duration of 5 milliseconds, a repetition period of 100 milliseconds, and a single-cycle square wave waveform. This method can simulate transient current fluctuations in power systems caused by sudden current loading, short circuits, or external impacts. Taking a high-temperature superconducting cable with a rated current of 3kA as an example, after inputting the pulse signal into the equivalent operating condition model, the model output automatically records data such as the current density, temperature field distribution, and magnetic flux changes inside the cable, and samples them with a time step of 10 microseconds to form a transient response time series with a length of 0.5 seconds. This time series reflects the entire process of the superconducting tape from steady state to disturbance and then back to steady state. It can be clearly observed that the temperature rises by about 2.3K during the pulse action, the current distribution shows a brief non-uniformity, and the magnetic flux lines are locally distorted, which provides a data basis for subsequent time and frequency analysis.

[0043] Secondly, after obtaining the transient response time series, empirical mode decomposition (EMD) is performed to extract intrinsic mode function components at different time scales. The specific process is as follows: First, local extrema in the response signal are identified, and upper and lower envelopes are constructed through interpolation to separate the main fluctuation components of the signal. This process is repeated to gradually extract several intrinsic mode function (IMF) components, each representing dynamic characteristics within a specific frequency range. Taking the current density time series as an example, six IMF components are obtained after decomposition. IMF1 corresponds to high-frequency rapid disturbances, reflecting the transient peak characteristics of the current; IMF3 and IMF4 correspond to mid-frequency energy components, revealing the energy transfer characteristics in the electromagnetic-thermal coupling process; and IMF6 represents low-frequency components, corresponding to the gradual trend of the system gradually recovering to a steady state. Subsequently, Hilbert transform is performed on each IMF component to obtain instantaneous frequency and energy amplitude information. The instantaneous frequencies and energy values ​​of all IMFs are combined along the time axis to form a time-frequency energy distribution matrix. The matrix presents a multi-peak energy distribution on the time and frequency axes, which can intuitively reflect the energy accumulation and propagation path of the quench event.

[0044] Furthermore, after obtaining the time-frequency energy distribution matrix, the quench trigger moment and its propagation path are identified using energy peak tracking and spatial correlation analysis. Specifically, the energy distribution of each time period is scanned to identify energy spikes and correlate them with the spatial node coordinates of the model to determine the initial location and timing of the quench. Taking actual simulation data as an example, approximately 8.6 milliseconds after applying a pulsed current signal, the energy density of the IMF3 component in the inner region of the superconducting tape in the matrix suddenly increases to 4.7 times the steady-state value, which is determined to be the quench trigger moment. Subsequently, within approximately 2.5 milliseconds, this high-energy region propagates outward along the spiral direction of the tape, with a propagation path length of approximately 30 mm and a corresponding propagation speed of approximately 12 mm / ms. Simultaneously, thermal field analysis results show that the temperature peak along this path gradually decreases, indicating that while the quench front diffuses towards the stable region, there is also a partial heat back-transfer effect. This method can accurately identify the quench trigger point, propagation direction, and propagation range, providing key parameters for subsequent response curve plotting.

[0045] Finally, after identifying the quench trigger moment and propagation path, a transient quench response characteristic curve was constructed to quantitatively characterize the dynamic features of the quench behavior. Specifically, the spatial coordinates corresponding to the energy peak were matched with the time point to calculate the trajectory of the quench front on the time axis, thus plotting the quench front velocity curve. Taking the aforementioned sample as an example, within the 10 to 15 milliseconds after pulse current triggering, the quench front velocity gradually decreased from the initial 15 mm / ms to 6 mm / ms, indicating that the system underwent a rapid diffusion and local self-recovery phase within a short period. Subsequently, the system recovery time curve, i.e., the time required from quench triggering to complete recovery from the superconducting state, was obtained through temperature and current recovery data. The recovery time was approximately 42 milliseconds, with a maximum temperature drop of approximately 2.1 K during the recovery process, and the current density redistribution tended to be uniform. Ultimately, based on the trends of these two curves, the dynamic response process of the cable in a quench event can be fully described, including the three stages of quench initiation, propagation, and recovery, providing a quantitative basis for subsequent control optimization and protection strategy design.

[0046] In this example, empirical mode decomposition is performed on the transient response time series to extract intrinsic mode function components, specifically as follows: Identify all extreme points of the transient response time series and construct the upper and lower envelopes; Calculate the mean of the upper and lower envelopes, and calculate the residual between the transient response time series and the mean; Repeat the above process until the residual satisfies the preset eigenmode function condition, and obtain the first eigenmode function component; Subtract the first intrinsic mode function component from the transient response time series to obtain the remaining series. Continue to decompose the remaining series until the remaining series is a monotonic function.

[0047] It should be noted that, in order to perform empirical mode decomposition on the transient response signal of the high-temperature superconducting cable, it is first necessary to identify extrema and construct the envelope of the transient response time series obtained from the equivalent model of the operating condition. Specifically, the time series is input into the signal analysis module, and all local maxima and minima in the signal are detected by a sliding window scanning method. Taking the sequence of current density changing with time as an example, a total of 286 extrema were identified in the range of 0-50 milliseconds, where the maxima correspond to the peaks of the pulse rising phase and the minima correspond to the valleys of the rapid current decay phase. Subsequently, using these maxima as anchor points, cubic spline interpolation is used to connect them sequentially to form the upper envelope; similarly, the lower envelope is constructed using the minima as anchor points. These upper and lower envelopes together define the overall envelope range of the signal fluctuation and can reflect the amplitude changes of local oscillations in the signal. Actual results show that the upper envelope peak rises rapidly between 5 and 10 milliseconds, indicating that the current response energy is concentrated at this time, while the lower envelope shows a significant dip in this range, forming the main oscillation segment of the transient signal.

[0048] Secondly, after constructing the upper and lower envelopes, this embodiment calculates the mean of the two envelopes at each time point to obtain the local central trend of the signal within that time interval. Subsequently, the original transient response time series is compared with this mean curve to obtain the residual signal between the two. Taking a real sample as an example, in the transient current response signal at 77K, the calculated mean curve shows a gentle upward trend in the 12-20 ms interval, while the original signal exhibits significant rapid oscillations within the same interval. The residual waveform obtained by subtracting the two is approximately 15%-20% of the amplitude of the original signal, mainly concentrated in the high-frequency components, representing the local perturbation characteristics of the signal. Through this operation, the trend term and oscillation term of the signal can be effectively separated, allowing subsequent mode extraction to focus only on the intrinsic oscillation mode without being affected by overall drift.

[0049] Furthermore, after calculating the residual signal, this embodiment continues to repeatedly perform the steps of extreme value identification, envelope construction, and mean calculation on the residual signal until the residual satisfies the preset intrinsic mode function (IMF) conditions. Specifically, the judgment criteria include: 1. The difference between the number of extreme points and the number of zero-crossing points in the entire time series does not exceed 1; 2. The mean of the upper and lower envelopes is close to zero at any time point. Taking the response sequence of the pulse current signal as an example, after 5 repeated screenings, the envelope symmetry of the residual waveform is basically stable, and the number of extreme points and zero-crossing points is consistent, satisfying the IMF judgment conditions. The first IMF component obtained at this time represents the component with the highest frequency and shortest duration in the signal, which usually corresponds to the high-frequency transient disturbance of the system. The actual results show that the energy peak of this IMF1 appears 7 milliseconds after the pulse is applied, and the duration is about 3 milliseconds, reflecting the fast magnetic flux response caused by the transient change in current, which is a typical high-frequency characteristic before quench triggering.

[0050] Finally, after obtaining the first intrinsic mode function component, it is subtracted from the original transient response time series to obtain the residual signal sequence. This residual sequence represents the low-frequency or mid-frequency components in the signal that were not separated. Subsequently, the same extreme value identification, envelope construction, mean calculation, and residual sieving steps as described above are performed on this residual sequence to gradually extract the second, third, and more IMF components. For example, in the superconducting cable signal analysis, a total of 6 IMF components and 1 residual term were extracted. IMF2 and IMF3 mainly reflect the energy coupling characteristics between the electromagnetic field and the thermal field, and their duration is relatively long, about 10-20 milliseconds; IMF5 and IMF6 represent the low-frequency components of the system during the slow recovery phase. As the decomposition progresses, the oscillating components of the residual signal gradually weaken. When the last residual signal no longer has local extreme values ​​and changes monotonically overall, the decomposition process is considered to be over. The final IMF components can reflect the dynamic behavior of the superconducting cable at different time scales, providing a fine-grained data foundation for identifying quench propagation and energy transfer paths.

[0051] S5. Based on the transient quench response characteristics, a multi-objective optimization function is constructed, and the NSGA-III algorithm is used to optimize the control parameters to obtain the optimal control strategy.

[0052] In this example, a multi-objective optimization function is constructed based on the transient quench response characteristics, and the NSGA-III algorithm is used to optimize the control parameters to obtain the optimal control strategy, specifically: Based on the transient quench response characteristics, a multi-objective optimization function is defined, which includes minimizing the quench response time, minimizing the peak temperature, and maximizing system stability. Initialize the control parameter population and set the parameter range; The NSGA-III algorithm is used for multi-objective optimization. In each generation, new individuals are generated by simulating crossover and mutation, and the multi-objective optimization function value of each new individual is calculated. The non-dominated level and crowding distance of each new individual are calculated based on the multi-objective optimization function value, and the optimal control strategy is selected based on the non-dominated level and crowding distance.

[0053] It should be noted that, firstly, based on the aforementioned transient quench response characteristics of the high-temperature superconducting cable, a multi-objective optimization function is constructed to comprehensively optimize the key control parameters of the system. This multi-objective optimization function aims to simultaneously consider three performance indicators: minimizing the quench response time, minimizing the peak temperature, and maximizing system stability. Minimizing the quench response time constrains the time required for the cable to recover from quench triggering to the superconducting state, reflecting the system's rapid recovery capability to sudden disturbances. Minimizing the peak temperature requires that the internal temperature of the cable does not exceed a safe critical value under any transient condition, thereby preventing localized ablation or permanent degradation. Maximizing system stability evaluates the cable's operational reliability in complex dynamic environments by examining the amplitude stability of temperature, current, and magnetic flux fluctuations in the multi-field coupling response. In the pulse current disturbance experiment, the initial quench response time was 46 milliseconds, the peak temperature reached 93 K, and the system stability index (based on response fluctuation amplitude evaluation) was 0.68. Based on this, the above three indicators are used as constraint functions for multi-objective optimization, and appropriate weights are assigned to achieve the operational goals of rapid, low-temperature rise, and stable operation. The definition of this multi-objective function is the core of the entire optimization process, used to guide subsequent parameter evolution and strategy selection.

[0054] Furthermore, after defining the optimization objective, an initial search space is provided for the NSGA-III algorithm by constructing a population of control parameters. Each individual in the control parameter population represents a set of potential system control strategies, containing key parameters affecting the cable's dynamic response, such as cooling flow rate, pulse current amplitude, thermal protection delay time, and the safety factor of the superconducting layer's critical current. Taking a typical operating condition as an example, the cooling flow rate is set to 1.0–2.5 L / min, the pulse current amplitude is 90%–130% of the rated current, the thermal protection delay time is set to 0.5–5 ms, and the safety factor of the critical current ranges from 0.7–1.0. Based on these ranges, an initial parameter population of 200 individuals is generated, with each individual's parameter combination randomly selected within the aforementioned range. To ensure the diversity of the search, the initial population undergoes uniform distribution testing, ensuring that the value distribution of all parameters covers the main areas of the design space. After this step, a set of initial control parameters that can comprehensively represent different operating strategies is obtained, laying the foundation for the evolution and optimization of the NSGA-III algorithm.

[0055] Furthermore, the NSGA-III algorithm is employed for multi-objective optimization of the control parameter population. During algorithm execution, each generation generates new individuals through simulated crossover and mutation operations to continuously explore better solutions. Specifically, several individuals in the population are randomly selected as "parents," and their control parameters are partially exchanged (simulated crossover), with one or more parameters randomly changed (mutation operation) to generate new "offspring" individuals. For example, in the 10th generation iteration, one individual is selected with a cooling flow rate of 1.8 L / min and a pulse current amplitude of 125%, while another individual has a cooling flow rate of 2.2 L / min and a pulse amplitude of 105%. The new individual generated after crossover has a cooling flow rate of 2.0 L / min and a pulse amplitude of 115%. Subsequently, a random mutation is applied to the thermal protection delay parameter of the offspring individual, changing it from 2 milliseconds to 1.5 milliseconds. The generated new individuals are then input into the equivalent operating condition model for simulation, and the corresponding quench response time, peak temperature, and stability index values ​​are calculated through the model. The system automatically records the multi-objective function results for each individual, forming the performance distribution of the current generation. As the number of iterations increases, the overall performance of the population gradually converges to the optimal region of the objective function.

[0056] Finally, after each generation of evolution, the population is ranked and crowding distance is calculated based on the multi-objective optimization results of individuals. The non-dominated ranking is used to compare the superiority of different individuals: if an individual is not inferior to another individual in all objectives and is superior to the other in at least one objective, it is said to "dominate" the latter. The algorithm classifies all non-dominated individuals into the first tier (non-dominated front), individuals dominated once into the second tier, and so on. Simultaneously, to prevent over-concentration on local optima, the "crowding distance" is calculated for individuals in each tier, which measures the distribution density of that individual relative to its surrounding individuals in the objective space. Individuals with larger distances are located in more open areas and can be retained to maintain population diversity. Taking the optimization results of the 30th generation as an example, there are 22 individuals in the first non-dominated front. Among them, 6 individuals have a quench response time of less than 30 milliseconds, a peak temperature of less than 85K, and a system stability higher than 0.9, and are selected as candidate optimal solutions. Finally, based on engineering application priorities (e.g., safety over response speed), the optimal control strategy was determined from the candidate solutions: cooling flow rate 2.1 L / min, pulse current amplitude 110%, thermal protection delay time 1.2 ms, and critical current safety factor 0.85. After simulation verification, this strategy reduced the quench response time to 27 ms, lowered the peak temperature to 84 K, and improved system stability to 0.93, significantly better than the initial settings, thus verifying the effectiveness and feasibility of the proposed method.

[0057] Example 2, Figure 2This invention presents an equivalent analysis system for high-temperature superconducting cables, comprising a model building module, a parameter optimization module, a fault simulation module, an equivalent analysis module, and an optimization control module. The model building module is used to collect the structural feature parameter set of high-temperature superconducting cables and build the first equivalent circuit model based on the structural feature parameter set; The parameter optimization module is used to perform cross-common screening of material parameters based on the first equivalent circuit model and adopt a multi-factor influence separation method to obtain the first equivalent parameter set. The fault simulation module is used to construct a first coupled model based on a first equivalent parameter set, and to apply disturbance signals of different frequencies to the first coupled model to simulate faults and obtain an equivalent model of the working condition. The equivalent analysis module is used to extract transient response data based on the equivalent model of the working condition, and to identify the transient quench response characteristics of the high-temperature superconducting cable based on the transient response data. The optimization control module is used to construct a multi-objective optimization function based on the transient quench response characteristics, and to optimize the control parameters using the NSGA-III algorithm to obtain the optimal control strategy.

[0058] The present invention also includes an electronic device, the electronic device comprising: At least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform an equivalent analysis method for a high-temperature superconducting cable.

[0059] The present invention also includes a computer-readable storage medium storing a computer program that, when executed by a processor, implements an equivalent analysis method for high-temperature superconducting cables.

[0060] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0061] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0062] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0063] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0064] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0065] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for equivalent analysis of high-temperature superconducting cables, characterized in that, Includes the following steps: A set of structural characteristic parameters of a high-temperature superconducting cable was collected, and a first equivalent circuit model was constructed based on the set of structural characteristic parameters. Based on the first equivalent circuit model, a multi-factor influence separation method was used to cross-screen the material parameters to obtain a first equivalent parameter set. A first coupling model was constructed based on the first equivalent parameter set, and fault simulation was performed by applying perturbation signals of different frequencies to the first coupling model to obtain an equivalent model under operating conditions. Transient response data was extracted based on the equivalent model under operating conditions, and the transient quench response characteristics of the high-temperature superconducting cable were identified based on the transient response data. A multi-objective optimization function is constructed based on the transient quench response characteristics, and the NSGA-III algorithm is used to optimize the control parameters to obtain the optimal control strategy.

2. The equivalent analysis method for high-temperature superconducting cables according to claim 1, characterized in that, The process involves collecting a set of structural characteristic parameters of the high-temperature superconducting cable and constructing a first equivalent circuit model based on this set of parameters. The geometric dimensions and material properties of the high-temperature superconducting cable were analyzed to obtain the diameter of the copper skeleton, the number of layers, width, thickness, winding angle, and temperature characteristics of the material resistivity. Calculate the resistance of the copper skeleton based on the diameter of the copper skeleton and the temperature characteristics of its resistivity. Calculate the equivalent resistance and equivalent inductance of each layer of superconducting tape based on the number of layers, width, thickness and orientation angle of the superconducting tape. Obtain the spatial relationship between each conductor layer and calculate the interlayer mutual inductance parameters based on the spatial relationship; Obtain the outer diameter and relative permittivity of the shielding layer and calculate the interlayer distributed capacitance; The first equivalent circuit model is constructed by integrating the copper frame resistor, equivalent resistance and equivalent inductance, interlayer mutual inductance parameters and interlayer distributed capacitance.

3. The equivalent analysis method for high-temperature superconducting cables according to claim 2, characterized in that, Based on the first equivalent circuit model, a multi-factor influence separation method is used to perform cross-commonality screening of material parameters to obtain the first equivalent parameter set, specifically: Multi-dimensional influencing factors of material parameters are extracted from the first equivalent circuit model, and a multi-factor influence separation matrix is ​​constructed. The multi-dimensional influencing factors include temperature change characteristics, current load rate and frequency response characteristics. Based on the multi-factor influence separation matrix, the multi-dimensional influence factors of each material parameter are mapped to the orthogonal feature space to obtain the mapped multi-dimensional influence factors. A cross-commonality screening algorithm was used to linearly evaluate the mapped multi-dimensional influence factors, and material parameters were screened based on the evaluation results to obtain the first equivalent parameter set.

4. The equivalent analysis method for high-temperature superconducting cables according to claim 3, characterized in that, The first coupling model is constructed based on the first equivalent parameter set, and fault simulation is performed by applying disturbance signals of different frequencies to the first coupling model to obtain the equivalent working condition model, specifically as follows: The first equivalent parameter set is mapped to the electromagnetic field, thermal field, and stress field to establish the field coupling equation; The field coupling equation is discretized to obtain the discretized field coupling equation, and the discretized field coupling equation is solved by the finite element method to obtain the first coupling model. A frequency sweep perturbation signal from low frequency to high frequency is applied to the first coupled model, and the dynamic response data of the first coupled model under each frequency sweep perturbation signal is obtained; Analyze the dynamic response data, extract fault characteristic patterns, and correct the parameters of the first coupled model based on the characteristic patterns to obtain the equivalent model of the working condition.

5. The equivalent analysis method for high-temperature superconducting cables according to claim 4, characterized in that, The process of extracting transient response data based on an equivalent operating condition model and identifying the transient quench response characteristics of high-temperature superconducting cables based on this data is as follows: A pulsed current signal is applied to the equivalent model of the working condition to construct a transient response time series; Empirical mode decomposition is performed on the transient response time series to extract the intrinsic mode function components and calculate the Hilbert spectrum of the intrinsic mode function components to obtain the time-frequency energy distribution matrix; Identify the quench trigger time and quench propagation path from the time-frequency energy distribution matrix; Based on the quench trigger time and propagation path, a transient quench response characteristic curve is plotted, which includes the quench leading edge velocity and recovery time.

6. The equivalent analysis method for high-temperature superconducting cables according to claim 5, characterized in that, The empirical mode decomposition of the transient response time series to extract intrinsic mode function components specifically involves: Identify all extreme points of the transient response time series and construct the upper and lower envelopes; Calculate the mean of the upper and lower envelopes, and calculate the residual between the transient response time series and the mean; Repeat the above process until the residual satisfies the preset eigenmode function condition, and obtain the first eigenmode function component; Subtract the first intrinsic mode function component from the transient response time series to obtain the remaining series. Continue to decompose the remaining series until the remaining series is a monotonic function.

7. The equivalent analysis method for high-temperature superconducting cables according to claim 6, characterized in that, The method involves constructing a multi-objective optimization function based on the transient quench response characteristics and using the NSGA-III algorithm to optimize the control parameters to obtain the optimal control strategy, specifically as follows: Based on the transient quench response characteristics, a multi-objective optimization function is defined, which includes minimizing the quench response time, minimizing the peak temperature, and maximizing system stability. Initialize the control parameter population and set the parameter range; The NSGA-III algorithm is used for multi-objective optimization. In each generation, new individuals are generated by simulating crossover and mutation, and the multi-objective optimization function value of each new individual is calculated. The non-dominated level and crowding distance of each new individual are calculated based on the multi-objective optimization function value, and the optimal control strategy is selected based on the non-dominated level and crowding distance.

8. A high-temperature superconducting cable equivalent analysis system, applied to the high-temperature superconducting cable equivalent analysis method according to any one of claims 1-7, characterized in that, It includes a model building module, a parameter optimization module, a fault simulation module, an equivalent analysis module, and an optimization control module: The model building module is used to collect the structural feature parameter set of high-temperature superconducting cables and build the first equivalent circuit model based on the structural feature parameter set; The parameter optimization module is used to perform cross-common screening of material parameters based on the first equivalent circuit model and adopt a multi-factor influence separation method to obtain the first equivalent parameter set. The fault simulation module is used to construct a first coupled model based on a first equivalent parameter set, and to apply disturbance signals of different frequencies to the first coupled model to simulate faults and obtain an equivalent model of the working condition. The equivalent analysis module is used to extract transient response data based on the equivalent model of the working condition, and to identify the transient quench response characteristics of the high-temperature superconducting cable based on the transient response data. The optimization control module is used to construct a multi-objective optimization function based on the transient quench response characteristics, and to optimize the control parameters using the NSGA-III algorithm to obtain the optimal control strategy.

9. An electronic device, characterized in that, The electronic device includes: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores a computer program that can be executed by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform an equivalent analysis method for high-temperature superconducting cables as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the equivalent analysis method for high-temperature superconducting cables as described in any one of claims 1 to 7.

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