A method, system, device and medium for modeling the electro-magnetic-thermal coupling characteristics of a high-temperature superconducting cable with a three-phase unified package structure

Abstract

This invention discloses a method, system, device, and medium for modeling the electro-magnetic-thermal coupling characteristics of a three-phase integrated high-temperature superconducting cable. The method includes: establishing an electrical model based on the equivalent circuit of parallel multilayer tapes; considering interlayer and interphase electromagnetic coupling in the current distribution model to obtain the current in each tape layer; establishing a critical characteristic and equivalent resistance calculation model using the gold extended model considering magnetic field anisotropy and combining it with power-law relations, and calculating AC losses; establishing a two-dimensional heat transfer model considering interlayer thermal resistance with AC losses as a heat source term, and correcting the circumferential non-uniform convection heat transfer conditions and interphase heat conduction channels through angular weighting functions and shape factors; iterating based on time parameters, feeding the temperature field and equivalent resistance back to the current distribution model to achieve closed-loop updates, and outputting electro-magnetic-thermal coupling simulation results, thereby providing a calculation model that more closely matches the actual operating conditions for the steady-state and fault condition simulation of a three-phase integrated high-temperature superconducting cable.

Description

Technical Field

[0001] This invention relates to the field of high-temperature superconducting cable modeling technology, and in particular to a method, system, equipment and medium for modeling the electro-magnetic-thermal coupling characteristics of a three-phase integrated high-temperature superconducting cable. Background Technology

[0002] High-temperature superconducting cables possess advantages such as high current density and low loss. They have demonstrated application potential in power distribution and transmission scenarios with tight power corridors and dense loads in urban core areas. However, their operational safety margin and fault tolerance are highly dependent on the coupling relationship between electrical parameters, magnetic field distribution, AC losses, and the temperature rise process. Existing research and engineering simulations typically use equivalent circuits or lumped parameter models to describe the parallel current shunting and resistance transition processes of superconducting tapes, and estimate AC losses using empirical loss models or simplified critical current degradation relationships. Furthermore, in thermal calculations, axisymmetric or uniform heat transfer boundaries are often used to approximate liquid nitrogen cooling conditions. While these existing methods have some applicability in single-phase or coaxial high-temperature superconducting cables, in three-phase integrated structures, due to their non-axisymmetric cross-section, stronger interphase and interlayer electromagnetic coupling, more complex magnetic field angle distribution at the tape, and significant circumferential differences in local heat transfer conditions, using simplified assumptions such as symmetrical boundaries and weak coupling provided by existing technologies can easily lead to significant errors in steady-state operation assessments and transient quench analyses.

[0003] Therefore, it is necessary to propose a modeling method for the electro-magnetic-thermal coupling characteristics of three-phase integrated structures, which can simultaneously reflect the equivalent parallel connection of multilayer tapes in superconducting cables, electromagnetic self-inductance and mutual inductance, magnetic field anisotropic loss mechanism, and the influence of non-axisymmetric heat transfer boundary on the temperature rise process, so as to improve the rationality of simulation of three-phase integrated high-temperature superconducting cables under steady-state and fault conditions. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides a method, system, device, and medium for modeling the electro-magnetic-thermal coupling characteristics of three-phase integrated high-temperature superconducting cables. The technical problems solved are: axisymmetric modeling errors caused by the non-axisymmetric cross-section and heat transfer boundary of three-phase integrated high-temperature superconducting cables, as well as steady-state operation assessment and transient quench analysis errors caused by factors such as significant interphase and interlayer electromagnetic coupling, complex magnetic field angle distribution, and obvious local heat transfer circumferential differences.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: In a first aspect, the present invention provides a method for modeling the electro-magnetic-thermal coupling characteristics of a three-phase integrated high-temperature superconducting cable, including: A current distribution model for a three-phase integrated high-temperature superconducting cable is established based on the equivalent circuit of multi-layer strip parallel connection. The interlayer and interphase electromagnetic coupling are taken into account in the current distribution model to obtain the current of each layer of strip. A critical characteristic and equivalent resistance calculation model is established by adopting the gold extended model that considers magnetic field anisotropy and combining it with the power law relationship, and the AC loss is calculated based on the current of each layer of the strip. A two-dimensional heat transfer model considering interlayer thermal resistance is established by taking the AC loss as a heat source term. An angular weighting function and a shape factor are introduced to correct the non-axisymmetric convective heat transfer boundary and the equivalent heat conduction path between phases of the overall structure to obtain the temperature field. Based on the time parameter, the temperature field and equivalent resistance are fed back to the current distribution model to achieve closed-loop update, and the electro-magnetic-thermal coupling simulation results are output.

[0007] As a preferred embodiment of the electro-magnetic-thermal coupling characteristic modeling method for a three-phase integrated high-temperature superconducting cable according to the present invention, wherein: the process of considering interlayer and interphase electromagnetic coupling in the current distribution model and obtaining the current of each layer of the strip includes: Based on the equivalent circuit of parallel multilayer tape, the conductor layer and shielding layer of the three-phase integrated high-temperature superconducting cable are divided into multiple parallel branches, and the current vector and common terminal voltage vector of the parallel branches are obtained. Construct an inductance matrix that includes the self-inductance terms of each branch and the mutual inductance terms between phases and between layers; The equivalent resistance of each branch is determined based on the current temperature field and magnetic field distribution, and then assembled into an equivalent resistance matrix. By combining the inductance matrix and the equivalent resistance matrix, the electromagnetic coupling equations of the parallel branches are established, and the current of each layer of the strip is obtained by solving the electromagnetic coupling equations of the parallel branches.

[0008] As a preferred embodiment of the electro-magnetic-thermal coupling characteristic modeling method for a three-phase integrated high-temperature superconducting cable described in this invention, the establishment of the critical characteristic and equivalent resistance calculation model includes: The critical current density is calculated using the gold extended model that considers magnetic field anisotropy. Based on the critical current density and the preset criterion electric field, a power-law relationship is established between the electric field strength and the current density. The equivalent resistivity of the superconducting layer is derived based on the aforementioned correspondence. The equivalent resistance of each parallel branch is calculated based on the equivalent resistivity of the superconducting layer.

[0009] The beneficial effects of this preferred technical solution are: it can more accurately describe the current distribution, magnetic field behavior and loss characteristics of a three-phase integrated high-temperature superconducting cable under a non-axisymmetric structure.

[0010] As a preferred embodiment of the electro-magnetic-thermal coupling characteristic modeling method for a three-phase integrated high-temperature superconducting cable described in this invention, the calculation of AC loss includes: Integrate the electric field strength and current density at each strip location over one power frequency cycle; The average value of the integral result over the power frequency period is calculated to obtain the AC loss per unit length. The AC loss per unit length is converted into a volumetric heat source term, which is then used as input to the two-dimensional heat transfer model.

[0011] As a preferred embodiment of the electro-magnetic-thermal coupling characteristic modeling method for a three-phase overlay structure high-temperature superconducting cable described in this invention, the method of introducing angular weighting functions and shape factors to correct the non-axisymmetric convective heat transfer boundary and the equivalent interphase heat conduction path of the overlay structure includes: The volumetric heat source term is input into the two-dimensional heat transfer model to establish a two-dimensional heat transfer control equation that takes into account the influence of interlayer thermal resistance. An angular weighting function is defined for the convective heat transfer boundary on the outer surface of the cable to adjust the local heat transfer coefficient according to the circumferential position, reflecting the non-axisymmetric cooling conditions. A shape factor is defined for the heat transfer path between different phases to correct the equivalent thermal resistance between phases, so as to reflect the influence of the non-axisymmetric geometry of the overall structure on the heat conduction path.

[0012] As a preferred embodiment of the electro-magnetic-thermal coupling characteristic modeling method for a three-phase integrated high-temperature superconducting cable described in this invention, the method for implementing closed-loop updates includes: At the current time step, based on the temperature field and magnetic field distribution of the previous time step, the equivalent resistance of each parallel branch is updated through the critical characteristics and equivalent resistance calculation model. The updated equivalent resistance matrix is ​​combined with the inductance matrix, and the current distribution of each layer of the strip in the current step is obtained by solving the electromagnetic coupling equation of the parallel branch. The magnetic field distribution is calculated based on the current distribution in the current step, and the volumetric heat source term is updated based on the current distribution and magnetic field distribution through the AC loss calculation model. The updated volumetric heat source term and the boundary conditions corrected by the angular weighting function and shape factor are input into the two-dimensional heat transfer control equations to solve for the temperature field of the current step. Repeat the update steps, sequentially updating the equivalent resistance, current distribution, heat source term and temperature field on the preset time iteration sequence to complete the dynamic closed-loop simulation of electro-magnetic-thermal coupling.

[0013] The beneficial effects of this preferred technical solution are: it significantly improves the simulation accuracy of steady-state operation and transient quenching process of cables, providing a reliable basis for cable design optimization and safe operation assessment.

[0014] As a preferred embodiment of the electro-magnetic-thermal coupling characteristic modeling method for a three-phase integrated high-temperature superconducting cable described in this invention, the output electro-magnetic-thermal coupling simulation results include: After the preset simulation time is reached, the output temperature rise evolution curve, hot spot location, current distribution of each layer of strip, AC loss distribution, and the update results of equivalent resistance over time are displayed. The quench region and start time are determined by the quench criterion.

[0015] Secondly, this invention provides a modeling system for the electro-magnetic-thermal coupling characteristics of a three-phase overlay structure high-temperature superconducting cable, comprising: An electromagnetic coupling module is used to establish a current distribution model for a three-phase integrated high-temperature superconducting cable based on a multi-layer strip parallel equivalent circuit, and to take into account inter-layer and inter-phase electromagnetic coupling in the current distribution model to obtain the current of each layer of strip. The loss and critical characteristic calculation module is used to establish a critical characteristic and equivalent resistance calculation model by adopting the gold extended model that considers magnetic field anisotropy and combining it with the power law relationship, and to calculate AC loss based on the current of each layer of strip. The non-axisymmetric heat transfer correction module is used to establish a two-dimensional heat transfer model that takes the AC loss as a heat source term and takes into account the interlayer thermal resistance. It also introduces angular weighting functions and shape factors to correct the non-axisymmetric convective heat transfer boundary and the equivalent heat conduction path between phases of the overall structure to obtain the temperature field. The iterative update module is used to iterate based on time parameters, feed the temperature field and equivalent resistance back to the current distribution model to achieve closed-loop update, and output the electro-magnetic-thermal coupling simulation results.

[0016] Thirdly, the present invention provides an electronic device, including a memory and a processor; the memory is used to store computer-executable instructions, and the processor executes the computer-executable instructions to implement the steps of a method for modeling the electro-magnetic-thermal coupling characteristics of a three-phase integrated high-temperature superconducting cable.

[0017] Fourthly, the present invention provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the steps of a method for modeling the electro-magnetic-thermal coupling characteristics of a three-phase overlay structure high-temperature superconducting cable.

[0018] Compared with existing technologies, the beneficial effects of this invention are as follows: Addressing the axisymmetric modeling error caused by the non-axisymmetric nature of the bundled cross section and heat transfer boundary, this invention utilizes the equivalent of parallel multilayer tapes and self-inductance and mutual inductance matrices to achieve phase-to-phase and interlayer electromagnetic coupling modeling. Furthermore, considering the anisotropic magnetic field, the Kim extended model and power-law relationship enable unified calculation of critical characteristics, equivalent resistance, and AC losses. This allows for a more accurate description of the current distribution, magnetic field behavior, and loss characteristics of three-phase bundled high-temperature superconducting cables under non-axisymmetric structures. This invention employs angular weighting functions and shape factors to correct the non-axisymmetric heat transfer boundary and interphase heat conduction channels. Combined with time-step closed-loop iteration, it achieves real-time updates of current distribution, equivalent resistance, losses, and temperature field, thereby significantly improving the simulation accuracy for steady-state operation and transient quenching processes of the cable. This provides a more realistic calculation model for the steady-state and fault condition simulation of three-phase bundled high-temperature superconducting cables. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of the overall process logic of a modeling method for the electro-magnetic-thermal coupling characteristics of a three-phase integrated high-temperature superconducting cable provided in an embodiment of the present invention.

[0021] Figure 2 This is a schematic diagram of a three-phase integrated structure for a modeling method of electro-magnetic-thermal coupling characteristics of a three-phase integrated high-temperature superconducting cable provided in an embodiment of the present invention. Detailed Implementation

[0022] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0023] Example 1, referring to Figure 1 As an embodiment of the present invention, a method for modeling the electro-magnetic-thermal coupling characteristics of a three-phase overlay structure high-temperature superconducting cable is provided, such as... Figure 1 The specific steps shown are as follows: S100: A current distribution model for a three-phase integrated high-temperature superconducting cable is established based on the equivalent circuit of multi-layer strip parallel connection, and the electromagnetic coupling between layers and phases is taken into account in the current distribution model to obtain the current of each layer of strip. S200: The gold extended model considering magnetic field anisotropy is adopted and the critical characteristic and equivalent resistance calculation model is established by combining the power law relationship, and the AC loss is calculated based on the current of each layer of strip. S300: A two-dimensional heat transfer model considering interlayer thermal resistance is established by taking AC loss as the heat source term, and the non-axisymmetric convective heat transfer boundary and the equivalent heat conduction path between phases of the overall structure are corrected by introducing angular weighting function and shape factor to obtain the temperature field. S400: Iterates based on time parameters, feeds back the temperature field and equivalent resistance to the current distribution model to achieve closed-loop update, and outputs electro-magnetic-thermal coupling simulation results.

[0024] It should be noted that, in response to the axisymmetric modeling errors caused by the non-axisymmetric cross-section and heat transfer boundary of the three-phase integrated high-temperature superconducting cable, as well as the steady-state operation assessment and transient quench analysis errors caused by factors such as significant interphase and interlayer electromagnetic coupling, complex magnetic field angle distribution, and obvious local heat transfer circumferential differences, this invention utilizes the equivalent of parallel multilayer tapes and the self-inductance and mutual inductance matrices to achieve interphase and interlayer electromagnetic coupling modeling. Furthermore, considering the anisotropy of the magnetic field, the Kim extended model and power-law relationship are used to achieve unified calculation of critical characteristics, equivalent resistance, and AC loss. This invention can more accurately describe the current distribution, magnetic field behavior, and loss characteristics of the three-phase integrated high-temperature superconducting cable under non-axisymmetric structures.

[0025] It should be noted that this invention uses angular weighting functions and shape factors to correct non-axisymmetric heat transfer boundaries and interphase heat conduction channels. Combined with time-step closed-loop iteration, it realizes real-time updates of current distribution, equivalent resistance, loss, and temperature field, thereby significantly improving the simulation accuracy of steady-state operation and transient quenching process of the cable. This provides a calculation model that is more in line with the actual operating conditions for the steady-state and fault condition simulation of three-phase integrated high-temperature superconducting cables.

[0026] Example 2, refer to Figure 2 Based on the previous embodiment, this embodiment provides a specific implementation method for modeling the electro-magnetic-thermal coupling characteristics of a three-phase integrated high-temperature superconducting cable, illustrating the technical means used in this method. For example... Figure 2 The three-phase integrated structure shown exhibits a non-axisymmetric distribution in cross-section, with significant interphase and interlayer electromagnetic coupling. The magnetic field angle distribution at the strip is complex, and the convective heat transfer conditions on the outer surface vary along the circumferential direction. It should be noted that the following parameter values ​​are examples or preferred ranges, used for ease of implementation and reproduction, and do not constitute a limitation on the scope of protection of this invention.

[0027] S100: A current distribution model for a three-phase integrated high-temperature superconducting cable is established based on the equivalent circuit of multi-layer strip parallel connection, and the electromagnetic coupling between layers and phases is taken into account in the current distribution model to obtain the current of each layer of strip. In this embodiment of the invention, the steps for obtaining the current of each layer of the strip include: Based on the equivalent circuit of multilayer tape parallel circuit, the conductor layer and shielding layer of the three-phase overlay structure high-temperature superconducting cable are divided into multiple parallel branches, and the current vector of the parallel branches is obtained. With common terminal voltage vector ; Construct an inductance matrix that includes the self-inductance terms of each branch and the mutual inductance terms between phases and between layers. ; The equivalent resistance of each branch is determined based on the current temperature and magnetic field distributions, and then assembled into an equivalent resistance matrix. ; By combining the inductance matrix and the equivalent resistance matrix, the electromagnetic coupling equations of the parallel branches are established, and the current of each layer of the strip is obtained by solving the electromagnetic coupling equations of the parallel branches.

[0028] Specifically, the specific formula for the electromagnetic coupling equation of the parallel branches is as follows: in, For the common terminal voltage vector of the parallel branches, For the parallel branch current vector, For an inductance matrix containing self-inductance and mutual inductance terms, The temperature of the superconducting layer. is the magnetic induction intensity vector.

[0029] It should be noted that the inductor matrix Preferably, the mutual inductance term is established based on unit length and consistent with the branch length in the calculation; the mutual inductance term is preferably obtained by analytical approximation or finite element extraction; initial temperature It is preferable to take a value near the liquid nitrogen inlet temperature, for example... or Initial equivalent resistance matrix The preferred approach is the power-law model described later. Calculated under the initial magnetic field conditions. As an example, the time-domain solution can employ implicit trapezoidal or backward Euler discretization, with a time step size of... Preferred to To balance stability and computational efficiency.

[0030] It should be noted that step S100 above, by establishing a current distribution model based on the parallel equivalent circuit of multilayer strips and taking into account the electromagnetic coupling between layers and phases, can accurately reflect the current distribution of each layer of strip in the three-phase integrated structure. This solves the problem of current distribution error caused by neglecting the coupling between phases and layers when the traditional axisymmetric model describes asymmetric structures, and lays the electrical foundation for the accurate calculation of subsequent losses and temperature rise.

[0031] S200: The gold extended model considering magnetic field anisotropy is adopted and the critical characteristic and equivalent resistance calculation model is established by combining the power law relationship, and the AC loss is calculated based on the current of each layer of strip. In this embodiment of the invention, the critical characteristic and equivalent resistance calculation model is established by using the gold extended model that considers magnetic field anisotropy and combining it with the power law relationship, including: The critical current density is calculated using the gold extended model that considers magnetic field anisotropy. Based on the critical current density and the preset criterion electric field, the correspondence between electric field strength and current density is established through a power law relationship. The equivalent resistivity of the superconducting layer is derived based on the corresponding relationship; The equivalent resistance of each parallel branch is calculated based on the equivalent resistivity of the superconducting layer.

[0032] Specifically, to describe the influence of the magnetic field angle distribution at the strip on the critical characteristics, an equivalent magnetic field expression considering magnetic field anisotropy is adopted, and the specific formula is as follows: in, This represents the equivalent magnetic field considering magnetic field anisotropy. Here are the anisotropy coefficients. Preferred selection to ; and These represent the perpendicular and parallel components of the magnetic field relative to the normal of the strip's wide face, respectively. Based on this, the critical current density is calculated using the Kim extended model, expressed by the following formula: in, The critical current density, The zero-field reference critical current density, The critical temperature. Temperature index The characteristic magnetic field constant is This is the magnetic field index.

[0033] For example, if the strip is a REBCO type material, the critical temperature is... Preferred selection to Temperature index Preferred selection to Characteristic magnetic field constant Preferred selection to Magnetic field index Preferred selection to .

[0034] Specifically, based on the critical current density and the preset criterion electric field, a power-law relationship is established between the electric field strength and the current density, as shown in the following formula: in, For electric field strength, To determine the electric field, For current density, For example, the power-law exponent. As an example, the criterion is the electric field. Preferred selection Power Law Index Preferred selection to .

[0035] Specifically, the equivalent resistivity of the superconducting layer is derived based on the relationship between electric field strength and current density: in, The equivalent resistivity of the superconducting layer. Convert to branch equivalent resistance or resistance per unit length for updating .

[0036] In an optional embodiment, the equivalent resistance of the parallel branch can also be calculated by integrating the equivalent resistivity of the superconducting layer along the conductive cross section of the strip and dividing it by the effective cross-sectional area, and then combining it with the axial length of the parallel branch to obtain the DC equivalent resistance of the branch.

[0037] In an optional embodiment, the equivalent resistance calculation of the parallel branch can also adopt a piecewise linearization method. Based on the local magnetic field and temperature conditions of the strip, the equivalent resistivity is discretized into several segments, the resistance of each segment is calculated separately, and the segments are connected in series or in parallel to obtain the branch equivalent resistance considering nonlinear distribution.

[0038] In this embodiment of the invention, calculating AC loss includes: Integrate the electric field strength and current density at each strip location over one power frequency cycle; The average value of the integral result over the power frequency cycle is calculated to obtain the AC loss per unit length. The AC loss per unit length is converted into a volumetric heat source term, which is then used as input to the two-dimensional heat transfer model.

[0039] Specifically, the formula for calculating AC loss per unit length is as follows: Furthermore, the AC loss per unit length is converted into a volumetric heat source term, expressed by the formula: in, Indicates the power frequency period, Represents the integral domain of the conductive cross section of the strip. This represents the heated volume per unit length.

[0040] In an optional embodiment, AC loss can also be calculated using the finite element electromagnetic simulation method, which directly solves Maxwell's equations in a three-dimensional or two-dimensional model to calculate the electromagnetic field distribution of the cable structure at power frequency, and obtains the accurate AC loss distribution through the Poynting vector method or the local Joule thermal integral method.

[0041] In an optional embodiment, the AC loss can also be calculated based on a critical state model, by directly calculating the hysteresis loss of the superconducting tape in an alternating magnetic field using analytical or numerical methods, and then superimposing the coupling loss to obtain the total AC loss.

[0042] It should be noted that step S200 above introduces the Kim extended model that considers magnetic field anisotropy and combines it with the power law relationship to establish a critical characteristic and equivalent resistance calculation model, which can more accurately characterize the critical current degradation behavior and nonlinear resistance characteristics of superconducting tape under complex magnetic field angles, thereby achieving refined calculation of AC loss.

[0043] S300: A two-dimensional heat transfer model considering interlayer thermal resistance is established by taking AC loss as the heat source term, and the non-axisymmetric convective heat transfer boundary and the equivalent heat conduction path between phases of the overall structure are corrected by introducing angular weighting function and shape factor to obtain the temperature field. In this embodiment of the invention, step S300 includes the following sub-steps A1 to A3: In A1: Input the volumetric heat source term into the two-dimensional heat transfer model to establish the two-dimensional heat transfer control equation that takes into account the influence of interlayer thermal resistance; Specifically, the obtained volumetric heat source term Input a two-dimensional heat transfer model and establish the two-dimensional heat transfer control equations that take into account the influence of interlayer thermal resistance. The specific formulas are as follows: in, For material density, For specific heat capacity, Radial coordinates, and These are the radial and axial thermal conductivity, respectively. Interlayer thermal resistance can be incorporated into the model through interface thermal resistance boundaries or equivalent thermal conductivity. As an example, the thermal conductivity of the metal layer can be taken as... and From tens to hundreds The order of magnitude, the thermal conductivity of the insulating layer can be taken as [value missing]. to The order of magnitude, and the specific value, should be determined according to the material handbook or experimental calibration.

[0044] In A2: Define an angular weighting function for the convective heat transfer boundary on the outer surface of the cable to adjust the local heat transfer coefficient according to the circumferential position, reflecting the non-axisymmetric cooling conditions; Specifically, to address the circumferential differences in convective heat transfer on the outer surface of the packaged structure, an angular weighting function is introduced to correct the convective boundary. The specific formula is as follows: in, The boundary equivalent thermal conductivity, For temperature gradient, The outward normal unit vector, Angular position The equivalent convective heat transfer coefficient at that point, The angular weighting function is... As the reference convective heat transfer coefficient, This is the temperature of liquid nitrogen.

[0045] For example, liquid nitrogen temperature Preferred selection to Reference convective heat transfer coefficient Preferred selection to Angular weighting function A piecewise constant can be used to represent the heat transfer differences in different circumferential sections, for example, in sections near the interphase gaps or cooling channels. to In the shaded section where heat exchange is relatively weak, the sample was taken. to .

[0046] In an optional embodiment, the correction of the non-axisymmetric convective heat transfer boundary can also be achieved by a mapping method based on thermal-fluid coupling simulation. The circumferential distribution of the heat transfer coefficient is obtained by performing a fluid dynamics simulation on the cooling channel in advance, and the distribution result is imported into the heat transfer model as a function table or fitted surface to assign boundary conditions.

[0047] In an optional embodiment, the correction of the non-axisymmetric convective heat transfer boundary can also introduce empirical correlations or correction factors related to the circumferential position to establish an expression for the heat transfer coefficient related to the angular position, dynamically reflecting the non-uniform cooling effect.

[0048] In A3: Define shape factors for the heat transfer paths between different phases to correct the equivalent thermal resistance between phases, so as to reflect the influence of the non-axisymmetric geometry of the overall structure on the heat conduction path; Specifically, to address the differences in heat conduction channels between phases, a shape factor is introduced to correct the equivalent thermal resistance between phases. The specific formula is as follows: in, For the sake of the prime minister With phase The equivalent thermal resistance after correction between them Based on the equivalent thermal resistance between phases, For shape factor, For the effective perimeter, For the axisymmetric equivalent perimeter. As an example, the shape factor. It can be constructed and normalized according to the ratio of interphase gap width to equivalent heat conduction path length, with a preferred value range of [value range missing]. to To cover the typical geometric differences in the overall cross-section.

[0049] It should be noted that step S300 above uses AC loss as an internal heat source and establishes a two-dimensional heat transfer model that takes into account interlayer thermal resistance. At the same time, it uses angular weighting functions and shape factors to correct the non-axisymmetric cooling boundary and interphase heat conduction path, which significantly improves the realism of the temperature field simulation and can effectively capture the uneven temperature distribution and hot spot formation caused by structural asymmetry and local heat transfer differences.

[0050] S400: Iterates based on time parameters, feeds back the temperature field and equivalent resistance to the current distribution model to achieve closed-loop update, and outputs electro-magnetic-thermal coupling simulation results; In this embodiment of the invention, the steps of iterating based on time parameters and feeding back the temperature field and equivalent resistance to the current distribution model to achieve closed-loop updates include: At the current time step, based on the temperature and magnetic field distributions of the previous time step, the equivalent resistance of each parallel branch is updated using the critical characteristics and equivalent resistance calculation model. By combining the updated equivalent resistance matrix with the inductance matrix, the current distribution of each layer of the strip in the current step is obtained by solving the electromagnetic coupling equation of the parallel branch. The magnetic field distribution is calculated based on the current distribution in the current step, and the volumetric heat source term is updated based on the current distribution and magnetic field distribution through the AC loss calculation model. The updated volumetric heat source term and the boundary conditions corrected by the angular weighting function and shape factor are input into the two-dimensional heat transfer control equations to solve for the temperature field of the current step. Repeat the update steps, sequentially updating the equivalent resistance, current distribution, heat source term and temperature field on the preset time iteration sequence to complete the dynamic closed-loop simulation of electro-magnetic-thermal coupling.

[0051] Specifically, in the Step to the first The steps are solved and updated sequentially according to the following relationships, with the specific formulas as follows: in, For the first The updated equivalent resistance matrix, For the first Step magnetic induction intensity distribution, Operators for solving electromagnetic equations Operators for solving the heat transfer equation, This is a mapping operator that updates the equivalent resistance matrix based on the temperature and magnetic field distributions. This is a mapping operator for calculating the volumetric heat source term from the magnetic field distribution and temperature field allocated by the current. For the first Step volume heat source term distribution, For the first Step equivalent heat transfer coefficient distribution, These are the spatial coordinates.

[0052] It should be noted that the convergence condition for the closed-loop iteration can be taken as the maximum change in the temperature field satisfying Or the change in the equivalent resistance matrix satisfies At least one of them.

[0053] In this embodiment of the invention, the output electro-magnetic-thermal coupling simulation results include: After reaching the preset simulation duration, the system outputs the temperature rise evolution curve, hotspot locations, current distribution across each strip layer, AC loss distribution, and the updated equivalent resistance over time. It also determines the quench region and its starting time using a quench criterion. As an example, a temperature criterion can be used as the quench criterion, with the specific formula as follows: in, For position At any time temperature, For position At any time The current density.

[0054] It should be noted that step S400 above achieves dynamic closed-loop coupling update between the temperature field, equivalent resistance and current distribution model through an iterative mechanism based on time parameters. This fully simulates the interaction process of multiple physical fields such as electricity, magnetism and heat in the spatiotemporal evolution, and significantly improves the simulation accuracy and prediction capability of the three-phase integrated high-temperature superconducting cable under steady-state and transient conditions and the quench boundary.

[0055] It should be noted that, without departing from the concept of the present invention, the above embodiments can be modified to adjust the discrete particle size of the strip branches. function form Construction method, The selection of the solver and the equivalent replacement of the solver implementation method should both fall within the protection scope of this invention.

[0056] Example 3: This example provides a modeling system for the electro-magnetic-thermal coupling characteristics of a three-phase overlay structure high-temperature superconducting cable, including: The electromagnetic coupling module is used to establish a current distribution model for a three-phase integrated high-temperature superconducting cable based on the equivalent circuit of multi-layer strip parallel connection, and to take into account the inter-layer and inter-phase electromagnetic coupling in the current distribution model to obtain the current of each layer of strip. The loss and critical characteristic calculation module is used to establish a critical characteristic and equivalent resistance calculation model by adopting the gold extended model that considers magnetic field anisotropy and combining it with the power law relationship, and to calculate AC loss based on the current of each layer of strip. The non-axisymmetric heat transfer correction module is used to establish a two-dimensional heat transfer model that takes AC loss as the heat source term and considers interlayer thermal resistance. It also introduces angular weighting functions and shape factors to correct the non-axisymmetric convective heat transfer boundary and the equivalent heat conduction path between phases of the overall structure to obtain the temperature field. The iterative update module is used to perform iterations based on time parameters, feed the temperature field and equivalent resistance back to the current distribution model to achieve closed-loop updates, and output the electro-magnetic-thermal coupling simulation results.

[0057] It should be noted that the technical solution of the electro-magnetic-thermal coupling characteristic modeling system for three-phase overlay high-temperature superconducting cables is based on the same concept as the technical solution of the electro-magnetic-thermal coupling characteristic modeling method for three-phase overlay high-temperature superconducting cables described above. For details not described in detail in the technical solution of the electro-magnetic-thermal coupling characteristic modeling system for three-phase overlay high-temperature superconducting cables in this embodiment, please refer to the description of the technical solution of the electro-magnetic-thermal coupling characteristic modeling method for three-phase overlay high-temperature superconducting cables described above.

[0058] The above-mentioned unit modules can be embedded in the processor of the electronic device in hardware form or independent of it, or they can be stored in the memory of the electronic device in software form, so that the processor can call and execute the corresponding operations of the above modules.

[0059] This embodiment also provides an electronic device, which includes a processor, a memory, a communication interface, a display screen, and an input device connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. When the computer program is executed by the processor, it implements a modeling method for the electro-magnetic-thermal coupling characteristics of a three-phase integrated high-temperature superconducting cable. The display screen can be a liquid crystal display (LCD) or an e-ink display. The input device can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the device's casing, or an external keyboard, touchpad, or mouse.

[0060] This embodiment also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method proposed in the above embodiments.

[0061] The storage medium proposed in this embodiment belongs to the same inventive concept as the method proposed in the above embodiments. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0062] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory, random access memory, flash memory, hard disk, or optical disk, and includes several instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) to execute the method of the embodiments of the present invention.

[0063] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the present invention.

Claims

1. A method of modeling the electro-magnetic-thermal coupling properties of a high temperature superconducting cable oriented to a three-phase unified package structure, characterized in that, include: A current distribution model for a three-phase integrated high-temperature superconducting cable is established based on the equivalent circuit of multi-layer strip parallel connection. The interlayer and interphase electromagnetic coupling are taken into account in the current distribution model to obtain the current of each layer of strip. A critical characteristic and equivalent resistance calculation model is established by adopting the gold extended model that considers magnetic field anisotropy and combining it with the power law relationship, and the AC loss is calculated based on the current of each layer of the strip. A two-dimensional heat transfer model considering interlayer thermal resistance is established by taking the AC loss as a heat source term. An angular weighting function and a shape factor are introduced to correct the non-axisymmetric convective heat transfer boundary and the equivalent heat conduction path between phases of the overall structure to obtain the temperature field. Based on the time parameter, the temperature field and equivalent resistance are fed back to the current distribution model to achieve closed-loop update, and the electro-magnetic-thermal coupling simulation results are output.

2. A method of modeling the electro-magnetic-thermal coupling properties of a high temperature superconducting cable in a three-phase unified package configuration according to claim 1, characterized in that, The process of taking into account interlayer and interphase electromagnetic coupling in the current distribution model to obtain the current of each strip layer includes: Based on the equivalent circuit of parallel multilayer tape, the conductor layer and shielding layer of the three-phase integrated high-temperature superconducting cable are divided into multiple parallel branches, and the current vector and common terminal voltage vector of the parallel branches are obtained. Construct an inductance matrix that includes the self-inductance terms of each branch and the mutual inductance terms between phases and between layers; The equivalent resistance of each branch is determined based on the current temperature field and magnetic field distribution, and then assembled into an equivalent resistance matrix. By combining the inductance matrix and the equivalent resistance matrix, the electromagnetic coupling equations of the parallel branches are established, and the current of each layer of the strip is obtained by solving the electromagnetic coupling equations of the parallel branches.

3. The method for modeling the electro-magnetic-thermal coupling characteristics of a three-phase overlay structure high-temperature superconducting cable as described in claim 2, characterized in that, The establishment of the critical characteristic and equivalent resistance calculation model includes: The critical current density is calculated using the gold extended model that considers magnetic field anisotropy. Based on the critical current density and the preset criterion electric field, a power-law relationship is established between the electric field strength and the current density. The equivalent resistivity of the superconducting layer is derived based on the aforementioned correspondence. The equivalent resistance of each parallel branch is calculated based on the equivalent resistivity of the superconducting layer.

4. The method for modeling the electro-magnetic-thermal coupling characteristics of a three-phase integrated high-temperature superconducting cable as described in claim 3, characterized in that, The calculation of AC loss includes: Integrate the electric field strength and current density at each strip location over one power frequency cycle; The average value of the integral result over the power frequency period is calculated to obtain the AC loss per unit length. The AC loss per unit length is converted into a volumetric heat source term, which is then used as input to the two-dimensional heat transfer model.

5. The method for modeling the electro-magnetic-thermal coupling characteristics of a three-phase integrated high-temperature superconducting cable as described in claim 4, characterized in that, The modification of the non-axisymmetric convective heat transfer boundary and interphase equivalent heat conduction path of the overall structure by introducing angular weighting functions and shape factors includes: The volumetric heat source term is input into the two-dimensional heat transfer model to establish a two-dimensional heat transfer control equation that takes into account the influence of interlayer thermal resistance. An angular weighting function is defined for the convective heat transfer boundary on the outer surface of the cable to adjust the local heat transfer coefficient according to the circumferential position, reflecting the non-axisymmetric cooling conditions. A shape factor is defined for the heat transfer path between different phases to correct the equivalent thermal resistance between phases, so as to reflect the influence of the non-axisymmetric geometry of the overall structure on the heat conduction path.

6. The method for modeling the electro-magnetic-thermal coupling characteristics of a three-phase integrated high-temperature superconducting cable as described in claim 5, characterized in that, The implementation of closed-loop update includes: At the current time step, based on the temperature field and magnetic field distribution of the previous time step, the equivalent resistance of each parallel branch is updated through the critical characteristics and equivalent resistance calculation model. The updated equivalent resistance matrix is ​​combined with the inductance matrix, and the current distribution of each layer of the strip in the current step is obtained by solving the electromagnetic coupling equation of the parallel branch. The magnetic field distribution is calculated based on the current distribution in the current step, and the volumetric heat source term is updated based on the current distribution and magnetic field distribution through the AC loss calculation model. The updated volumetric heat source term and the boundary conditions corrected by the angular weighting function and shape factor are input into the two-dimensional heat transfer control equation to solve for the temperature field of the current step. Repeat the update steps, sequentially updating the equivalent resistance, current distribution, heat source term and temperature field on the preset time iteration sequence to complete the dynamic closed-loop simulation of electro-magnetic-thermal coupling.

7. The method for modeling the electro-magnetic-thermal coupling characteristics of a three-phase integrated high-temperature superconducting cable as described in claim 6, characterized in that, The output electro-magnetic-thermal coupling simulation results include: After the preset simulation time is reached, the output temperature rise evolution curve, hot spot location, current distribution of each layer of strip, AC loss distribution, and the update results of equivalent resistance over time are displayed. The quench region and start time are determined by the quench criterion.

8. A modeling system for the electro-magnetic-thermal coupling characteristics of a three-phase overlay high-temperature superconducting cable, employing the electro-magnetic-thermal coupling characteristic modeling method for a three-phase overlay high-temperature superconducting cable as described in any one of claims 1 to 7, characterized in that, include: An electromagnetic coupling module is used to establish a current distribution model for a three-phase integrated high-temperature superconducting cable based on a multi-layer strip parallel equivalent circuit, and to take into account inter-layer and inter-phase electromagnetic coupling in the current distribution model to obtain the current of each layer of strip. The loss and critical characteristic calculation module is used to establish a critical characteristic and equivalent resistance calculation model by adopting the gold extended model that considers magnetic field anisotropy and combining it with the power law relationship, and to calculate AC loss based on the current of each layer of strip. The non-axisymmetric heat transfer correction module is used to establish a two-dimensional heat transfer model that takes the AC loss as a heat source term and takes into account the interlayer thermal resistance. It also introduces angular weighting functions and shape factors to correct the non-axisymmetric convective heat transfer boundary and the equivalent heat conduction path between phases of the overall structure to obtain the temperature field. The iterative update module is used to iterate based on time parameters, feed the temperature field and equivalent resistance back to the current distribution model to achieve closed-loop update, and output the electro-magnetic-thermal coupling simulation results.

9. An electronic device comprising a memory and a processor, characterized in that: The memory is used to store computer-executable instructions, and when the processor executes the computer-executable instructions, it implements the steps of the electro-magnetic-thermal coupling characteristic modeling method for a three-phase integrated high-temperature superconducting cable as described in any one of claims 1 to 7.

10. A computer-readable storage medium having computer-executable instructions stored thereon, characterized in that: When the computer-executable instructions are executed by the processor, they implement the steps of the electro-magnetic-thermal coupling characteristic modeling method for a three-phase integrated high-temperature superconducting cable as described in any one of claims 1 to 7.

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