Rapid three-dimensional electromagnetic simulation method and verification device for large uninsulated coil

Abstract

The invention discloses a rapid three-dimensional electromagnetic simulation method and verification device for a large-scale uninsulated coil, and aims to solve the problems of large calculation load, difficulty in homogenization, poor field-circuit coupling convergence and low result precision of the three-dimensional simulation of the existing large-scale uninsulated coil. The simulation method comprises the following steps: establishing a homogenized coil which does not divide specific turns, and setting anisotropic resistivity; constructing a current source area intercepted on the coil body and a free turn-to-turn resistance area connected in parallel with the current source area; applying current source excitation according to an open loop / closed loop coil; and the precision is ensured through radial grid encryption and result convergence verification. The verification device comprises a three-dimensional multi-turn verification coil, a direct current source, a multi-direction alternating external field applying module and a voltage and magnetic field measuring unit, direct current is supplied, an alternating external field is applied, and the simulation accuracy is measured and verified in real time. The method is simplified in modeling, rapid in calculation, good in convergence and high in precision, adapts to open-loop / closed-loop and single-cake / multi-cake coils, and is suitable for large uninsulated superconducting coils in rotary and linear motors, nuclear fusion equipment and the like.

Description

Technical Field

[0001] This invention relates to the field of superconducting electrical engineering technology, and in particular to a method and verification device for rapid three-dimensional electromagnetic simulation of large-scale uninsulated coils. Background Technology

[0002] In the field of superconducting electrics, uninsulated superconducting coils play a crucial role as specially designed electromagnetic components. These coils are made by winding superconducting wires without inter-turn insulation, primarily using superconducting ribbon wires, known as superconducting tape. The design principle of uninsulated coils is based on the near-zero resistance exhibited by superconducting materials under DC operating conditions. This allows current to flow mainly along the coil's circumferential direction, while the minute resistance generated by the metal layers in the multi-layered structure of the superconducting tape and the contact layers between the tapes creates natural inter-turn insulation. By removing the insulation layer, uninsulated coils offer greater compactness and current carrying capacity, as well as better inter-turn heat dissipation. Furthermore, when a point in the coil overheats and loses its superconducting properties, the current can bypass the heated point through the uninsulated inter-turn path, preventing further expansion of the heat source. Uninsulated coils are widely used in superconducting magnetic systems requiring DC current, such as powerful magnets, nuclear fusion tokamak devices, superconducting motors, and electric magnetic levitation systems.

[0003] Currently, the design and analysis of uninsulated coils mainly rely on two-dimensional and limited three-dimensional simulation methods. Existing two-dimensional simulation methods can homogenize and merge multi-turn coils, and can simulate the electromagnetic behavior of large coils to a certain extent. However, their limitation is that they cannot accurately reflect the current distribution and electromagnetic field changes in three-dimensional space, especially when dealing with complex working conditions such as alternating external fields. It is currently difficult to replicate this method into a three-dimensional model while maintaining its effectiveness.

[0004] Although existing literature has proposed three-dimensional finite element simulation models for uninsulated HTS coils, such as "Fast and accurate 3D FEM model for electromagnetic simulations of no-insulation HTS coils based on polygon-anisotropic-resistivity" in Volume 37, Issue 9 of Superconductor Science and Technology and "Modeling of contact resistivity and simplification of 3D homogenization strategy for the H formulation" in Volume 37, Issue 7, these methods still require detailed depiction of each turn of the coil and its helical structure during modeling. This leads to a sharp increase in computational load and a significant decrease in simulation efficiency when dealing with large coils.

[0005] Furthermore, while existing circuit models can describe current flow in uninsulated coils, they are difficult to perform three-dimensional simulations of such coils. Meanwhile, common field-circuit coupling models attempt to solve the problem through bidirectional coupling between the circuit model and the electromagnetic finite element model. However, under three-dimensional conditions, this bidirectional coupling leads to slow computation speed, poor convergence, and abnormal fluctuations in results under high-frequency alternating external fields, making it difficult to meet the fast and accurate simulation requirements of practical engineering applications.

[0006] In summary, the existing technology has the following technical problems: 1. Large computational load: Existing 3D simulation methods require detailed modeling of each turn of the coil when dealing with large uninsulated coils, resulting in a huge computational load and excessively long simulation time, which makes it difficult to meet the rapid design requirements in actual engineering.

[0007] 2. Poor convergence: Field-path coupling models are prone to convergence problems in 3D simulations, especially under the action of high-frequency alternating external fields, which increases the instability in the iterative calculation process and leads to distortion of simulation results.

[0008] 3. Limited accuracy: Although the two-dimensional simulation method has a small computational load, it cannot accurately reflect the current distribution and electromagnetic field changes in three-dimensional space. Especially when dealing with complex boundary conditions and alternating external fields, the simulation accuracy is severely affected.

[0009] To address the aforementioned issues, this invention proposes a rapid three-dimensional electromagnetic simulation method and verification device for large-scale uninsulated coils. This aims to fill the gap in existing technologies for three-dimensional simulation of large-scale uninsulated coils, improve simulation speed and accuracy, enhance the model's generalization ability, and provide strong support for the optimized design of uninsulated coils. Summary of the Invention

[0010] The technical problem to be solved by this invention is to provide a rapid three-dimensional electromagnetic simulation method and verification device for large uninsulated coils, which solves the problems of large computational load, difficulty in achieving uniformity, poor coupling convergence and insufficient current distribution accuracy in existing three-dimensional simulation technology for large uninsulated coils. It fills the technical gap in rapid three-dimensional simulation of ultra-large uninsulated coils, and provides a three-dimensional simulation method that takes into account the simplicity of modeling, computational efficiency and simulation accuracy, and designs a verification device to ensure the reliability of the simulation model.

[0011] To achieve the above-mentioned technical objectives, the present invention adopts the following technical solution: I. Simulation Methods This invention enables rapid simulation of large uninsulated coils. The main approach involves uniformizing each turn of the large uninsulated coil along the coil's radial direction, blurring the boundaries between turns. This avoids the complexity of modeling a large number of turns and significantly improves simulation speed. The specific steps are as follows: Step 1: Establish a uniform coil electromagnetic control model First, a uniform geometric model of the coil is constructed, without distinguishing the specific turns inside the coil, and the coil as a whole is regarded as a continuous uniform body.

[0012] Simultaneously, electromagnetic simulation control equations are established to describe the coupling relationship between the magnetic field, electric field, and current density. These electromagnetic simulation control equations include, but are not limited to: (1); In the formula, An Ampere loop expressing the relationship between magnetic field and current density; This is the law of electromagnetic induction; Ohm's law relationship between electric field and current density; For the Laplace operator, The magnetic field strength, For electric field strength, For current density, For external current density, Permeability, is the resistivity.

[0013] Step 2: Construct key functional areas based on equivalence theory This invention aims to establish a simulation model capable of homogenizing along the radial direction of the coil without needing to divide each turn. The specific equivalent process includes: Circuit theory model establishment: A circuit theory model of the uninsulated coil is established. This model is only used for the construction of equivalent theory and equivalent process, and is not adopted as the final simulation calculation model of this invention. Specifically, it includes the conductors of each turn of the coil, the inter-turn contact resistance between turns, and the current source connected to the end of the coil.

[0014] Concentrated equivalent of inter-turn resistance: The discrete inter-turn resistance distributed throughout the entire loop of the coil is concentrated and compressed into a fixed position in a certain loop, thus eliminating the interference of the distributed characteristics of the inter-turn resistance on the modeling. Reconfiguration of electrical connections between turns: Cut the physical wire connection between the Nth turn and the (N+1th)th turn of the coil, and reconnect the cut end to the Nth turn itself; if the coil is connected to an external current source (open-loop coil), add an insertion current source at the reconfiguration node with the same current value as the end current source; if the coil ends are short-circuited (closed-loop coil), constrain the current values ​​of the nodes before and after reconfiguration to keep them consistent, ensuring that the circuits before and after reconfiguration are equivalent. The formation of the homogenization model: After eliminating the series connection between each turn along the length of the conductor, the obstacle to the homogenization of each turn is also removed. Along the radial direction of the coil, the coil body, the concentrated inter-turn resistance and the current source on the node are homogenized.

[0015] Each turn of wire is uniformized and merged along the radial direction of the coil to form a coil body region that is a uniform block.

[0016] For open-loop coils, through the previous "turn-to-turn electrical connection reconstruction", there is now a node current source on each turn. The current sources are uniformized and merged along the radial direction to form a "current source region" sector cut off from the coil body. The size of this region should be as small as possible to ensure that the coil body is sufficiently preserved to closely resemble reality.

[0017] For a closed-loop coil, through the previous "turn-to-turn electrical connection reconstruction", there is now a node on each turn, and each such node is constrained to have equal current. These nodes are also merged along the radial direction of the coil to form a sector cut off from the coil body, which is also called the "current source region" for consistency. The size of this region should be as small as possible to ensure that the coil body is sufficiently preserved to closely resemble reality.

[0018] Similarly, through the previous "reconfiguration of the electrical connection between turns", each turn now has an inter-turn resistor connected to itself. These inter-turn resistors are also merged radially to form a separate "inter-turn resistance region" that is independent of the coil body, and this inter-turn resistance region is connected in parallel with the current source region.

[0019] Step 3: Set the anisotropic resistivity Since the inter-turn path has been equivalently replaced by the "inter-turn resistance region," the coil body only needs to retain the circumferential and axial current paths. Therefore, an anisotropic resistivity is set for the homogenized coil body: Radial (inter-turn direction) resistivity Set to the maximum value, close to insulation, to block radial current flow within the coil body; Circumferential resistivity (along the length of the conductor) Let the resistivity be defined as the resistivity along the length of the superconducting tape, and the axial resistivity as the resistivity along the width of the conductor. Set the resistivity in the width direction of the superconducting tape to ensure that the current flows in the actual conduction direction; To achieve the aforementioned anisotropic resistivity, the electric field strength in the coil region... E With current density J The relationship between them can be defined as follows: (2); To enable commercial software to recognize the expression, it needs to be transformed into a Cartesian coordinate system. The specific process is as follows: (3); Substituting (3) into (2) yields: (4); In the formula, , , These represent the electric field strengths along the radial, circumferential, and axial directions of the coil, respectively. , , The current density is measured in the radial, circumferential, and axial directions of the coil. The angle between the length direction of the conductor and the y-axis of the Cartesian coordinate system; , , These are the components of the electric field intensity in the Cartesian coordinate system. , , These are the current density components in the Cartesian coordinate system.

[0020] If the coil (such as a circular or racetrack-shaped coil) contains arcs or curved edges, these areas must be modeled as polygons with straight edges. In this way, the conductor length direction vector within each sector of the polygon is constant, thus allowing for the setting of the conductor length direction vector within each sector. The angular variable (i.e., the angle between the conductor length direction vector and the y-axis) is a constant that remains unchanged at all locations in space, allowing even a first-order, single-grid system to accurately describe the region within each sector. The use of angular variables reduces the requirements for the mesh.

[0021] Step 4: Apply excitation conditions to the current source region Based on the "open-loop / closed-loop" type of the coil, the external current density of the current source region is set accordingly. This ensures that the excitation matches the actual "open-loop / closed-loop" operating conditions of the coil. Simultaneously, the current source region... , , All values ​​are set to relatively large values ​​to avoid generating additional uncontrollable current in this region, ensuring that the current density in this region is controllable and equal to the applied external current density. .

[0022] Open-loop coil (ends connected to an external current source): The current density in the constrained current source region is equal to the external current density. According to step 2, the external current density set in the current source region. The required output current and external current density are equivalent to those of an end current source connected to an actual coil. The expression is: (5); In the formula, , , These represent the external current densities in the coil turns direction, circumferential direction, and axial direction, respectively. The current supplied to the current source connected to the end of the actual coil; It is the cross-sectional area through which a circumferential current can flow in a single or single-turn superconducting wire as a whole.

[0023] Closed-loop coil (ends short-circuited): The current source area is also configured similarly. , , It is a relatively large value, but No fixed value is set. According to step 2, the current source region does not need to be constrained to a specific current density value, but only needs to be constrained to have a uniform current distribution along the radial direction of the coil. However, such constraints are rare in actual simulation software. To achieve this, the present invention constrains the current in the current source region not to be equal to an actual value, but to be equal to the sum of the total ampere-turns of the coil circumferential current (obtained by integrating the circumferential current density on any cross section of the coil body through which the circumferential current can flow) and the total ampere-turns of the inter-turn current (obtained by integrating the circumferential current density on any cross section of the inter-turn resistance region through which the circumferential current can flow), divided by the cross-sectional area of ​​the coil as a whole through which the circumferential current can flow. This allows us to constrain the current to be uniformly distributed radially without limiting its magnitude, thus aligning with the characteristic of a closed-loop coil without an external power source. (External current density) Represented as: (6); In the formula, This refers to the total ampere-turns of the coil's circumferential current. This refers to the total ampere-turns of the coil's inter-turn current. This is the total cross-sectional area of ​​the coil, that is, the cross-sectional area of ​​all the turns in the coil.

[0024] Multi-pane closed-loop coil: According to step 2, even with a multi-pane closed-loop coil, it is still necessary to ensure that all nodes formed after the "electrical connection reconfiguration" on each pane are equal to each other. In this case, (6) needs to be improved, and the external current density between each pane needs to be considered additionally. They are all equal, therefore the external current density constraining the current source region of each pie is all the same and equal to the average of the sum of the circumferential current and the inter-turn current of each pie. Specifically The numerical values ​​satisfy: (7); In the formula, This represents the number of coils contained in the coil. The serial number represents the thread.

[0025] Step 5: Equivalently set the resistivity of the inter-turn resistance region To accurately simulate the actual inter-turn contact resistance in the "inter-turn resistance region," its resistivity parameters are derived based on the classical resistivity formula: First, the inter-turn interface resistivity (unit Converted to single-turn contact resistance : (9); In the formula, The inter-turn contact area of ​​a complete turn at a certain radial position of the coil can be calculated from the radial position; Then the discrete Equivalent to the continuous circumferential resistivity of the inter-turn resistance region The formula is: (8); In the formula, The circumferential length of the inter-turn resistance region; Simultaneously, the radial resistivity of the inter-turn resistance region... With axial resistivity Set to a larger value (for insulation) to avoid interference caused by induced current, and set a low-resistance lead. , Extremely small (Insulation to prevent induced current) Connect the inter-turn resistance area and the current source area to ensure normal current flow and form a parallel connection between the inter-turn resistance area and the current source area.

[0026] Step 6: Mesh generation and calculation accuracy verification Since the radial distribution accuracy of the circumferential and inter-turn currents of the homogenized coil depends entirely on the radial grid density, simulation accuracy needs to be ensured through "grid refinement - result convergence verification": Gradually increase the radial mesh density of the coil, and calculate key simulation indicators (such as circumferential current, electromagnetic loss, and magnetic field distribution) after each densification. If the simulation results gradually converge to a fixed value as the mesh density increases, then the mesh accuracy is sufficient; if the simulation results still show a rapid changing trend, then the mesh needs to be further refined.

[0027] II. Supporting Verification Device To verify the accuracy and reliability of the above simulation method, this invention also designs a large-scale, uninsulated coil, rapid three-dimensional electromagnetic simulation verification device, the specific structure and verification logic of which are as follows: 1. Device Composition Verification coil: Select a non-insulated superconducting coil with a typical three-dimensional structure (such as a racetrack-shaped coil) and a large number of turns (simulating a large coil scenario); Current source module: supplies DC current to the verification coil to simulate the DC operating conditions of the coil during normal operation; Alternating external field application module: Composed of a transformer and a magnet, the magnet direction can be adjusted to apply an alternating external field in any direction, covering the complex magnetic field environment that the coil may actually face, and exciting the three-dimensional effect of the coil; Measurement module: includes a voltage measurement unit based on a nanovoltmeter (for accurate measurement of coil voltage) and a magnetic field measurement unit based on a Hall probe and a gaussmeter (for real-time monitoring of coil magnetic field distribution).

[0028] 2. Verification Logic The performance of the simulation model was verified from multiple dimensions by using a combination of DC current application, alternating external field application, and real-time measurement. Verifying the current density distribution: The interaction between DC and alternating magnetic fields in superconducting tapes will change the current density distribution along the width of the tape and generate resistance. The accuracy of the current density distribution in the simulation can be verified by measuring the voltage. Verifying current branch distribution: The redistribution of circumferential / inter-turn current caused by the resistance of the strip will affect the voltage and magnetic field. By measuring the voltage and magnetic field together, the rationality of the current branch distribution in the simulation can be verified. In particular, once the current changes from the circumferential branch to the inter-turn branch, it will no longer generate the axial magnetic field at the center of the coil. By measuring the axial magnetic field at the center of the coil, the redistribution of current in the circumferential branch and the inter-turn branch in the coil can be accurately reflected. Verifying transient characteristics: The redistribution of current in the circumferential branches and inter-turn branches involves transient processes, resulting in transient processes in the measured voltage and magnetic field. The time constant of this transient process is related to the coil inductance and resistance. By measuring the transient process, the accuracy of the inductance and resistance parameters in the simulation can be verified. In addition, the transient characteristic measurement can also reflect the induced current generated in the coil under the alternating external field. This induced current changes instantaneously, and the generated magnetic field will resist the external alternating magnetic field. Therefore, the induced current can be reflected by magnetic field measurement. In an uninsulated coil, this induced current flows through the closed loop formed by the circumferential and inter-turn contacts of each turn.

[0029] Verification of three-dimensional effects: Applying an asymmetric magnetic field to excite the three-dimensional characteristics of the coil avoids damage to the coil caused by local thermal excitation, while achieving a refined verification of the simulation capability of three-dimensional effects.

[0030] The rapid three-dimensional electromagnetic simulation method and verification device for large-scale uninsulated coils provided by this invention have the following beneficial effects: 1. This invention effectively solves the problems of high computational load, difficulty in achieving uniformity, poor coupling convergence, and insufficient current distribution accuracy in existing large-scale uninsulated coil 3D simulation technology. It fills the gap in rapid 3D simulation technology for ultra-large uninsulated coils, and provides a 3D simulation method that balances modeling simplicity, computational efficiency, and simulation accuracy. It also includes a matching verification device to ensure the reliability of the simulation model, providing solid technical support for the research and development and application of ultra-large uninsulated coils.

[0031] 2. This invention does not require establishing discrete geometry and connection relationships for each turn of the coil. It only requires establishing a uniform coil geometry and refining the mesh radially, which greatly simplifies the preprocessing process. It breaks through the limitation of traditional 3D simulation requiring turn-by-turn modeling, reduces the workload of geometric modeling and boundary condition setting, and makes the originally cumbersome modeling process efficient and fast, greatly improving the efficiency of the overall simulation work.

[0032] 3. This invention eliminates the computational load caused by a large number of turns through homogenization, significantly improving the simulation speed and supporting rapid simulation of large coils with thousands of turns. It can meet the urgent need for rapid and accurate simulation of large coils and save a lot of time and costs for practical engineering applications.

[0033] 4. This invention abandons the field-circuit coupling model, eliminating the need for real-time field-circuit coupling iteration and real-time three-dimensional integration calculation (such as calculating the circumferential voltage / resistance of each element in the finite element field model), thus significantly improving the simulation speed.

[0034] 5. This invention abandons the field-circuit coupling model, fundamentally avoiding problems such as non-convergence, high-frequency result fluctuations, and result distortion caused by coupling, ensuring stable and reliable simulation results, and providing a highly reliable data foundation for subsequent coil design and optimization work based on simulation results.

[0035] 6. The uniform model of this invention makes the current continuously distributed along the radial direction. Compared with the discrete and different current distributions of each unit in other models such as field-circuit coupling, it is closer to the real physical scene and has a higher resolution of current distribution.

[0036] 7. This invention can be adapted to different types of large uninsulated coils such as open-loop / closed-loop and single-pane / multi-pane, and can simulate complex working conditions such as charging and discharging, quenching failure, and alternating external fields. The three-dimensional model can fully consider the non-uniform current density distribution in various dimensions, meet the actual application needs of superconducting electric fields (such as nuclear fusion tokamak and electric maglev), and has wide applicability and powerful functions.

[0037] 8. This invention also constructs a multi-physics field coupling simulation framework for electromagnetic and thermal fields, integrates electromagnetic loss analysis and thermal stability assessment modules, innovates the multi-physics field coupling architecture, realizes real-time bidirectional data transmission of electromagnetic-thermal coupling, and can comprehensively consider the influence of various factors such as electromagnetic and thermal factors on the performance of large uninsulated coils, providing a more complete solution for the comprehensive performance evaluation of coils.

[0038] 9. This invention solves the problem that two-dimensional simulation cannot accurately reflect the current distribution and electromagnetic field changes in three-dimensional space. It can realistically present the current distribution and dynamic changes of electromagnetic field in three-dimensional space, providing a powerful tool for in-depth understanding of the three-dimensional characteristics of large uninsulated coils. Attached Figure Description

[0039] Figure 1 This is a schematic diagram illustrating the derivation steps of the rapid three-dimensional simulation method in Embodiments 1 to 4 of the present invention; Figure 2 This is a schematic diagram illustrating the derivation steps of the rapid three-dimensional simulation methods in Embodiments 2 and 4 of the present invention; Figure 3 This is a schematic diagram illustrating the implementation of the rapid three-dimensional simulation method for large (closed-loop) uninsulated coils in embodiments 1, 3, and 4 of the present invention in finite element software. Figure 4 This is a flowchart illustrating the rapid three-dimensional simulation methods in Embodiments 3 and 5 of the present invention; Figure 5 This is a schematic diagram of the coil geometry mesh modeling in Embodiment 6 of the present invention; Figure 6 This is a diagram showing the change of circumferential current over time and the distribution of circumferential current density during the coil charging process in Embodiment 6 of the present invention. Figure 7 This is a diagram showing the electromagnetic loss and circumferential current density distribution of the coil in Embodiment 6 of the present invention under a transverse alternating external field; Figure 8 This is a diagram showing the electromagnetic loss and circumferential current density distribution of the coil in Embodiment 6 of the present invention under an axial alternating external field; Figure 9 This is a diagram showing the electromagnetic loss and circumferential current density distribution of the coil under local hot spot quench in Embodiment 6 of the present invention. Figure 10 This is a diagram showing the circumferential current decay of the closed-loop coil under alternating lateral and axial external fields in Embodiment 6 of the present invention. Figure 11 This is a schematic diagram of the geometry and mesh division of the large coil in Embodiment 7 of the present invention; Figure 12 This is a diagram showing the result of the coil circumferential current during the charging process of the large coil in Embodiment 7 of the present invention; Figure 13 This is a diagram showing the coil density distribution after the large coil in Embodiment 7 of the present invention has been fully charged. Figure 14 This is a diagram showing the coil circumferential current attenuation result of a large closed-loop coil under an alternating external field in Embodiment 7 of the present invention; Figure 15 This is a diagram showing the circumferential current density distribution of the large closed-loop coil under an alternating external field in Embodiment 7 of the present invention. Figure 16 This is a schematic diagram of the arrangement of the verification device in Embodiment 8 of the present invention. Detailed Implementation

[0040] To facilitate technical personnel's understanding of the technical solutions of the embodiments of this application, the technical terms will be introduced first.

[0041] (1) High-temperature superconducting tape: The internal structure is multi-layered, consisting of a superconducting layer sandwiched between multiple metal layers.

[0042] (2) Uninsulated coils: These are mostly used in the field of superconducting electric vehicles. They are formed by winding high-temperature superconducting tapes into coils without any inter-turn insulation. Therefore, there are two current flow paths in uninsulated coils: circumferential branches and inter-turn branches. Under normal DC current operation, uninsulated superconducting coils can ensure that the current flows only along the length of the conductor and along the circumferential direction of the coil. This is because the resistivity of the superconducting layer in the high-temperature superconducting tape is extremely low, so the surrounding metal layer is sufficient to form insulation, confining the current to flow only in the superconducting layer and preventing inter-turn current from being generated. However, uninsulated coils actually have two current flow branches: the circumferential branch and the inter-turn branch. In many operating conditions, current flows through both branches of an uninsulated coil, making it impossible to treat it the same as an insulated coil. For example: ① During coil charging and discharging, the changing current along the length of the superconducting conductor causes an inductive voltage drop, squeezing the current in the circumferential branch to the inter-turn branch. At this point, the inter-turn resistivity plays a decisive role in the current distribution. ② The resistance generated by quenching in the superconducting material, or the resistance generated by the superconducting material under an alternating external field (mechanically termed dynamic resistance), greatly increases the circumferential resistance of the coil, squeezing the coil current from the circumferential branch to the inter-turn branch. In this case, the current density distribution along the width of the superconducting strip also needs to be considered. ③ The axial alternating external field induces current in the closed loop formed by each turn and its inter-turn contacts. The advantages of uninsulated coils are: ④ Without an insulating layer, the coil is more compact and has a higher magnetic flux density. ⑤ When quenching occurs, the current can bypass the quenching point through the inter-turn branch, preventing the quench from worsening.

[0043] (3) Closed-loop coil: Superconducting DC coils can operate without a power supply. This is achieved by short-circuiting the ends of the superconducting coil using superconducting tape or connectors. In this case, the DC current inside the coil will flow continuously in the closed loop. This is because there are almost no losses in the superconducting coil, resulting in minimal decay and loss of the DC current over time. The advantages of closed-loop coils are: ① Good portability, allowing operation without a power supply; ② No need to connect to a power supply at room temperature through current leads, resulting in less heat leakage.

[0044] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments: Example 1 This embodiment provides a rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils, specifically describing the derivation principle and steps of the proposed rapid simulation method. Figure 1 The equivalent circuit schematic is used for illustration, but this does not mean that the finite element simulation method provided by this invention will involve any circuit model calculation.

[0045] Step 1.1, refer to Figure 1 , Figure 1(a) is the equivalent circuit of an uninsulated coil with a three-dimensional racetrack-shaped structure, where the turns are connected by inter-turn contact resistance, and there is distributed inductance and resistance in the coil loop (ignored in the figure). A current source is connected to the end of the coil. It can be seen that to simulate an uninsulated coil, each turn needs to be modeled. However, to achieve simulation of a large coil, it is necessary to avoid simulating a large number of turns and to uniformize the turns in the radial direction.

[0046] Step 1.2, further, will Figure 1 In (a), the inter-turn resistances distributed across the entire circumference are all lumped together into one, forming Figure 1 The circuit model in (b). This approximation method is theoretically reasonable; a more mature lumped approach in similar fields is to... Figure 1 (a) The lumped set is equivalent to Figure 1 (b) The diagram within the pink box forms a so-called moderate model, whose simulation reliability has been verified in many scenarios. This is based on the fact that existing research has found that regardless of the impedance generated in an uninsulated coil... Figure 1 Even at points where current is concentrated in a localized manner (a), the distribution of circumferential current and inter-turn current along the coil loops remains nearly uniform, therefore it can be considered that... Figure 1 (a) The inter-turn resistance of the coil coil distributed upwards is equivalent to: Figure 1 (b) Lumped-type inter-turn resistance.

[0047] Step 1.3, Figure 1 (b) Redraw it geometrically to obtain Figure 1 (c).

[0048] Step 1.4, further, discovered Figure 1 In (c), the currents at positions ①②③ are all equal and equal to the current of the current source. Therefore, a current source is artificially introduced at these positions to form... Figure 1 (d). It can be observed that, Figure 1 (d) and Figure 1 The current distribution in (c) is equivalent and there is no difference.

[0049] Step 1.5: According to circuit principles, as long as the current distribution before and after is consistent, any node can be cut off and reconnected to another node with an equal current magnitude. Therefore, in Figure 1 Cut the wire at the location marked with scissors in (d), and connect the cut wire to the current source of the previous turn to obtain... Figure 1 (e). It can be observed that, Figure 1 (e) and Figure 1The current distribution in (d) is equivalent. This measure ensures that the turns are no longer connected in series along the length of the conductor, but are independent, laying the groundwork for uniformizing all turns in the future.

[0050] Step 1.6: Since there are no longer any single-strand series connections between the turns, each turn can be uniformized radially to obtain... Figure 1 (f) This form can be directly established in the finite element model. It can be observed that a region, represented in blue, is defined on the coil, containing current sources. Since there are no longer boundaries between turns, the discrete current sources within the blue region will be represented by an external current density set within that region. For the discrete inter-turn resistance, an additional geometry with a specific resistivity will be established to represent it; this geometry is independent of the coil body and connected in parallel with the current sources.

[0051] Step 1.7: Because the radial inter-turn flow path has been equivalently expressed by the inter-turn resistance, no inter-turn flow path is set in the coil body. The radial resistivity of the coil area is set to a value close to that of insulation (which makes it possible to...). Figure 1 (f) and Figure 1 (e) equivalent), while the circumferential resistivity of the coil is still the resistivity along the length of the superconducting wire.

[0052] The reason why the finite element model provided by this invention can quickly simulate large uninsulated coils with a large number of turns is that it uses... Figure 1 (a) shows a coil with individual turns and an internally "discrete" structure, which is transformed into... Figure 1 (f) shows a coil that consists of only a homogenized body and has an internally "continuous" structure. The core step in achieving this equivalent lies in... Figure 1 In (d), based on circuit theory, the series connection between turns along the length of the conductor is broken, so that the model does not need to establish the specific turns and can be uniformized.

[0053] Example 2 In another preferred embodiment, based on the above embodiment 1, this embodiment provides a closed-loop method for rapid three-dimensional electromagnetic simulation of large uninsulated coils, as detailed below.

[0054] Example 1 provides a rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils. However, due to the connection of a current source, this model is an open-loop coil that is constantly connected to the current source. The following section will build upon this method by adding the ability to simulate a closed-loop coil, thus forming a closed-loop uninsulated coil simulation method.

[0055] Step 1: The derivation steps of the specific simulation method are as follows: Figure 2 As shown, where Figure 2 (a)-(c) and Figure 1 (a)-(c) are basically the same, the difference being that the ends of the closed-loop coil are not connected to a current source, but are directly shorted by superconducting tape.

[0056] Step 2, as follows Figure 1 As shown in (d), according to circuit principles, the nodes marked in blue have equal current magnitudes. They can be cut and reconnected, while ensuring that the current magnitudes of the nodes remain equal after reconnection, guaranteeing that the current distribution remains unchanged before and after the equivalence. Based on these equivalences, we obtain... Figure 2 (e). It can be observed that, Figure 2 The blue dot in (d) becomes after being cut and reconnected. Figure 2 The red dot in (e), and the original Figure 2 The current at each blue dot in (d) is equal, therefore, in order to make Figure 2 (e) and Figure 2 (d) Equivalent, then in Figure 2 (e) constrains the current at each red dot to be equal.

[0057] Step 3: Similarly, to achieve large-scale coil simulation, the coil needs to be homogenized radially to obtain... Figure 2 (f). The blue area represents the current source region, consisting of a portion of the coil body. To make... Figure 2 (f) and Figure 2 (e) Equivalently, it is necessary to constrain the current density distribution in the blue region to be uniform along the radial direction.

[0058] Step 4: Similarly, since the radial inter-turn flow path has been equivalently expressed by the inter-turn resistance, no inter-turn flow path is set within the coil body. The radial resistivity of the coil region is set to a value close to that of insulation (which makes it possible to...). Figure 2 (f) and Figure 2 (e) equivalent), while the circumferential resistivity of the coil is still the resistivity along the length of the superconducting wire.

[0059] Example 3 In another preferred embodiment, based on Embodiment 1 above, this embodiment provides a rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils, specifically describing the finite element implementation method and steps of the large-scale uninsulated coil simulation method of the present invention, based on... Figure 1 The structure in (f) can be used to establish a finite element model. The modeling steps are as follows: This embodiment demonstrates the use of COMSOL simulation software as an example, but the simulation method provided by this invention can be applied to simulation software other than COMSOL.

[0060] Step 1: Establish the coil geometry in the simulation software, such as... Figure 3As shown, the geometry of the uninsulated coil model includes: the superconducting coil body region, the current source region, the inter-turn resistance region, and the connecting lead region.

[0061] Step 2: In this superconducting electromagnetic simulation model, the governing equation is the commonly used H equation: (1).

[0062] Step 3, according to Figure 1 The schematic diagram in (f) should be set up Figure 3 The resistivity of the coil in the radial direction (i.e. ) is extremely large, close to insulating, while the circumferential resistivity (i.e. ) is still set as the resistivity along the length of the superconducting wire, and the axial resistivity (i.e. The resistivity is still set to the width direction of the superconducting wire. To achieve this resistivity setting, the coil region... Governing equations (i.e.) )as follows: (2); in, , , and , , These represent the electric field strength and current density along the radial, circumferential, and axial directions of the coil, respectively. Equation (2) is then transformed into a Cartesian coordinate system that can be input and recognized by the finite element software. Specifically, the following equation is used to replace [[ in equation (2)]. , , ]and[ , , ]: (3); Obtain the coil region The governing equations are: (4); in Angles such as Figure 3 The figure shows the angle between the length direction of the superconducting wire and the y-axis of the Cartesian coordinate system. It can be calculated based on the geometry of the superconducting coil. The mathematical principle is relatively basic and will not be elaborated on here.

[0063] If we assume that the arc edge of the coil is infinitely smooth, then The angle value should vary throughout the circular arc region. However, according to finite element theory, the angle value varies within each subdivided mesh. The spatial distribution of angular variable values ​​is expressed by interpolation functions, which have limited accuracy. Therefore, in the finite element model... The angle value cannot precisely match the preset value, which will cause the anisotropic resistivity set in the actual finite element model to deviate from the expected value, thus causing errors in the simulation results.

[0064] To solve the above problem, the infinitely smooth circular arc edge of the coil is modeled as a polygon, for example... Figure 3 The single semicircular arc shown is modeled with 12 sides. Correspondingly, at this time... The angle also becomes the angle between the tangent of the polygon and the y-axis, rather than the angle between the tangent of the arc and the y-axis. Therefore, the actual angle within each sector (represented by a trapezoidal geometric region) is... The angle values ​​are constant and do not change with location, making it possible to model an element even when using a first-order element mesh internally. The spatial distribution of variables is expressed by linear interpolation, which also yields accurate results. The angular simulation calculation value makes the anisotropic resistivity matrix (see formula (4)) accurate.

[0065] Step 4: For the superconducting coil body, the circumferential resistivity and axial resistivity and All values ​​are set as the resistivity of the superconducting wire, and are the overall resistivity of the superconducting wire after homogenizing the multi-layer structure inside the wire (see the previous technical term "high-temperature superconducting tape").

[0066] In most cases, the resistivity of the metal layer in parallel with the superconducting layer in a superconducting tape is considered negligible due to its high resistivity. Therefore, the overall resistivity of the superconducting tape is... and for: (10); in, To distribute the critical current density in a superconducting material evenly along its thickness across the entire superconducting tape, the calculation method is as follows: The critical current density is calculated from the overall critical current of the superconducting tape. Divide by the overall cross-sectional area of ​​the superconducting tape S (Including all layers in the superconducting tape).

[0067] In a few cases, the metal layer connected in parallel with the superconducting layer needs to be considered, such as when the resistance of the superconducting layer is very high after it loses quench. Since simulation models cannot model individual layers due to computational constraints, it is necessary to treat the multiple layers as a whole, considering the overall material resistivity (i.e., the overall material resistivity). or () is obtained by the parallel combination of the resistivities of the superconducting layer and the metal layer: (11); in, This represents the percentage of the superconducting layer in the composition of all layers in the entire tape. This represents the percentage of the metal layer in the total composition of all layers in the strip. To homogenize the resistivity of the superconducting layer to the value of the entire superconducting tape region, similarly... The resistivity of the metal layer is uniformized to the value of the entire superconducting tape region. The principle of uniformization is that the overall resistance of the superconducting tape after uniformization is the same as the overall resistance of the superconducting tape of the actual multilayer structure in the model.

[0068] The resistivity of the superconducting layer is: (12); in, Let be the current density in the superconducting layer. To obtain its specific value, solve the following equation: (13); in, Let be the current density in the metal layer. The physical implication behind this equation is that the voltage drop across the superconducting layer and the metal layer are equal, while due to... and Since all values ​​are unknown, the formula can be further transformed into: (14); in, This represents the current density in the superconducting layer distributed along the thickness direction across the entire superconducting tape. The current density in the metal layer is distributed along the thickness direction across the entire superconducting tape, and the two together constitute the overall current density modulus on the coil in the finite element model. And because the model does not have ,so Further transformation yields: (15); It can be observed that only in this formula For unknown variables, and These are variables that can be directly calculated in the finite element model. Therefore, the current density in the superconducting layer can be calculated in real time using formula (15). Thus, all resistivity in the coil can be calculated using formulas (11) and (12).

[0069] Optionally, in the case of electromagnetic-thermal multiphysics coupling, the electromagnetic loss density in the uninsulated coil is controlled by... The calculated temperature is then passed to the thermal field model, which in turn obtains the temperature. T The following formula affects the critical current density of the uninsulated coil in the electromagnetic model, and thus the resistivity of the superconducting wire: (16); Step 5: To apply the current source, you can do so in the finite element software. Figure 3 An external current density is applied to the current source region shown. To achieve an output current density equal to the set external current density, this region must be configured. , and All are maximum values, close to insulation (e.g., all set to 1). This avoids the generation of other types of current densities and ensures that the current density in the current source region is consistent with the artificially set external current density. The external current density of the current source region is then set. The expression is: (5); in, , , These represent the external current densities in the coil turns direction, circumferential direction, and axial direction, respectively. The current supplied by the current source connected in series at the ends of the coil in actual conditions; It is the cross-sectional area through which a circumferential current can flow in a single superconducting wire.

[0070] Step 6: To simulate the inter-turn path of an uninsulated coil, it is necessary to set up the appropriate configuration. Figure 3 The resistivity of the inter-turn resistance region shown allows it to be used as an equivalent measure of the contact resistance between coil turns.

[0071] Generally speaking, the interfacial resistivity between turns The unit is This is converted into the contact resistance between individual turns. See Figure 1 (b), the unit is ( The size expression is: (9); in, This is the inter-turn contact area at a certain radial position of the coil. Its size only changes with the radial position of the coil and can be easily calculated from the radial position of the coil.

[0072] In order to make Figure 3 The inter-turn resistance region in the middle can express Figure 1 (f) According to the classical resistivity formula, the inter-turn resistivity of this region along the coil loop direction is set as follows: (8); in, The circumferential length of the inter-turn resistance region; The cross-sectional area of ​​a single superconducting wire is equal to ,in The cross-sectional area of ​​the coil through which circumferential current can flow. This represents the total number of turns in the coil. This formula represents the discrete inter-turn resistance. (See Figure 1 (f) is equivalent to the continuous resistivity of the inter-turn resistance region. (See Figure 3 ).

[0073] Example 4 In another preferred embodiment, based on the above embodiments 2 and 3, this embodiment provides a rapid three-dimensional electromagnetic simulation method for large uninsulated coils, specifically describing the finite element implementation steps of the large closed-loop uninsulated coil simulation method of the present invention.

[0074] When implemented in finite element simulation software Figure 2 (f) In this method, finite element software typically lacks the ability to constrain the uniformity of current density distribution within a given region. To achieve this, a current source (external current density) is artificially inserted, ensuring that the current density distribution within the blue region is artificially predetermined and uniform along the coil's radial direction. The external current density within this blue region cannot be artificially assigned a fixed value; otherwise, the final simulation result will approximate an open-loop coil connected to a current source, i.e., close to... Figure 1 (f). Therefore, the external current density should be given as a variable without a specific numerical value or practical significance: (6); In the formula, The total ampere-turns of the coil circumferential current, the integration region is... Figure 3 A cross-section on the coil body marked; The total ampere-turns of the coil inter-turn current, the integration region is... Figure 3 A cross-section on the marked inter-turn resistance area; This is the specific value of the coil's cross-sectional area. Through formula (6), it is possible to determine the value without constraints. Figure 3 With a specific value for the current density in the blue region, the closed-loop coil simulation is achieved by simply constraining the current density in the blue region to be equal along the radial direction.

[0075] For multi-coil coils, external current density constraints need to be applied to the current source regions of all coils. for: (7); in, This represents the total number of coils in the coil. The number represents the coil number. This formula constrains the current density in the current source region of all coils to be the same, thus achieving closed-loop multi-coil simulation.

[0076] Example 5 In another preferred embodiment, based on embodiments 1 to 4 above, this embodiment provides a method for rapid three-dimensional electromagnetic simulation of large-scale uninsulated coils, the implementation steps of which are as follows: Figure 4 As shown. It's important to note that since the geometry of this model is a homogenized body in the radial direction of the coil, the resolution of the radial distribution of circumferential and inter-turn currents in the coil is determined solely by the radial mesh density. Therefore, multiple mesh refinements are required before calculation to verify whether the key simulation parameters converge with mesh refinement: if the gradient of the simulation results becomes stable with mesh refinement and no longer changes significantly, it is considered that the convergence interval has been reached, and the mesh accuracy is achieved; if the gradient of the simulation results remains steep with mesh refinement and still changes significantly, it is considered that the convergence interval has not been reached, and further mesh refinement is required.

[0077] Example 6 In another preferred embodiment, based on embodiments 1 to 7 above, this embodiment provides a fast three-dimensional electromagnetic simulation method for large-scale uninsulated coils, comparing the results of the simulation method proposed in this invention with those of existing methods. Existing methods use a polygonal anisotropic resistivity model, which can be found in the literature, specifically in "Fast and accurate 3D FEMmodel for electromagnetic simulations of no-insulation HTS coils based on polygon-anisotropic-resistivity" in Volume 37, Issue 9 of *Superconductor Science and Technology*. The effectiveness of this model in simulating uninsulated coils has been sufficiently verified in the literature through numerous simulations and experiments. The basic principle of this model is to establish the true helical geometry of the uninsulated coil, and then set the resistivity of the superconducting wire along the length direction and the inter-turn contact resistivity along the turn direction. Unlike the simulation method proposed in this invention, this traditional model always requires clearly representing each turn of the superconducting wire with a mesh, and cannot perform any uniform simplification. In the following verification process, the results obtained by the simulation method proposed in this invention are also compared with the relatively mature results found in the aforementioned paper.

[0078] The three-dimensional electromagnetic finite element simulation model proposed in this invention was built in COMSOL Multiphysics, specifically using the mfh module, which can fully express the governing equation, i.e., formula (1). The inter-turn resistivity of the uninsulated coil was set to 100. To achieve an accurate comparison with traditional models, a method consistent with traditional models is adopted: each turn of the coil is divided into one grid along its radial direction. The simulation model established based on the method proposed in this invention is as follows: Figure 5 As shown in Tables 1 and 2, the simulation examples are based on the operating conditions.

[0079] Table 1 Simulation verification examples of uninsulated coils

[0080] Table 2. Simulation verification examples of closed-loop uninsulated coils

[0081] Figure 6 The simulation results obtained in Example 1 include a comparison between the simulation method proposed in this invention and the traditional method. It can be observed that the circumferential current obtained from the two models exhibits good consistency in its time-varying behavior.

[0082] Figure 7 The simulation results for Example 2 include a comparison between the simulation method proposed in this invention and the traditional method. It can be observed that the electromagnetic loss waveforms of the coils simulated by the two models under a transverse alternating external field exhibit good consistency.

[0083] Figure 8 The simulation results obtained in Example 3 include a comparison between the simulation method proposed in this invention and the traditional method. It can be found that the electromagnetic loss waveforms of the coils simulated by the two models under an axial alternating external field show good consistency.

[0084] Figure 9 The simulation results obtained in Example 4 include a comparison between the simulation method proposed in this invention and the traditional method. It can be observed that the electromagnetic loss waveforms of the coil under local hotspot quench conditions obtained from the two models exhibit good consistency.

[0085] Figure 10 The simulation results obtained from Examples 5 and 6 include a comparison between the simulation method proposed in this invention and existing methods. It can be found that the current decay waveforms of the closed-loop coils simulated by the two models under transverse alternating external fields and axial alternating external fields show good consistency.

[0086] Example 7 In another preferred embodiment, based on embodiments 1 to 6 above, this embodiment provides a rapid three-dimensional electromagnetic simulation method for a large uninsulated coil. This embodiment will simulate a large closed-loop uninsulated coil with a very large number of turns based on the simulation method proposed in this invention, thereby demonstrating the effects of this invention. The large uninsulated coil comprises 8 discs, each disc having 750 turns, and the inter-turn resistivity of the coil is 200 Ω. Configure each coil as described above. Simultaneously, the grid division within the coil should be as follows: Figure 11 As shown, each disc has a grid density of 15 along the axial direction (i.e., the strip width direction) and a grid density of 20 along the radial direction.

[0087] The first simulation case focuses on an open-loop coil. Specifically, a linearly increasing current is introduced using a current source, and the phenomenon of a delay in the circumferential current in the coil compared to the power supply current is observed due to the current flowing into the inter-turn branches. The results are shown in [Figure Number]. Figure 12 The simulation results are consistent with common sense. Figure 13 The normalized current density distribution of the large uninsulated coil after charging, obtained by the simulation method of this invention, was found to conform to widely accepted physical laws. Specifically, positive and negative shielding currents appeared in the top and bottom coils, generated by the magnetic field on the larger vertical strip surface at these locations, while the middle coil exhibited a skin effect. In this example, the total simulation time was 8 hours, using an Intel i-14900 K computer chip, which is within an acceptable range.

[0088] The second simulation case focuses on the closed-loop coil, specifically operating it under a transverse alternating external field with a DC current flowing through it. The current attenuation due to electromagnetic losses is observed, and the specific results are as follows: Figure 14 As shown in the diagram, due to the applied alternating external field, resistive losses are generated in the closed-loop uninsulated coil, consuming the magnetic energy within it. Since there is no real-time power supply to replenish the magnetic energy, the current in the closed-loop uninsulated coil exhibits a decreasing trend. The normalized current density distribution is shown in the diagram. Figure 15 As shown, the alternating magnetic field induced a current density in the uninsulated coil, a phenomenon consistent with common sense. In this example, the simulation time was 20 minutes per alternating cycle, using an Intel i-14900 K computer chip, which is within an acceptable range.

[0089] It can be observed that the simulation time of the above examples is within an acceptable range. Since existing traditional models cannot accomplish the above tasks, no verification control group was included in the simulation results. It can be seen that, based on the method proposed in this invention, a large coil can be modeled as a uniform whole in the radial direction, without any geometric units. This brings the following advantages: ① It is not necessary to draw all 750 turns of the coil; instead, a uniform body is simulated, avoiding the slow simulation speed caused by a large number of turns; ② Although the radial direction of the coil still needs to be refined in the subsequent mesh generation stage, no geometric units need to be divided, thus saving a significant amount of geometric modeling work and the work of applying constraints / excitation conditions to a large number of divided geometric bodies, greatly simplifying the model construction process.

[0090] Example 8 In another preferred embodiment, based on embodiments 1 to 7 above, this embodiment provides a large-scale, uninsulated coil rapid three-dimensional electromagnetic simulation verification device, such as... Figure 16 As shown. According to the verification requirements, the device comprises the following parts: A typical three-dimensional structure (such as a racetrack-shaped coil) with a large number of turns was selected as the verification object. A current source was used to supply direct current to the uninsulated coil. An alternating external field excitation was applied using a transformer connected to a magnet. Depending on the direction of the magnet, the alternating magnetic field could be applied in any direction. Coil voltage measurement based on a nanovoltmeter and coil magnetic field measurement based on a Hall probe and a gaussmeter were selected.

[0091] The device was verified by passing a DC current through the coil and applying an alternating magnetic field, while simultaneously measuring the coil voltage and magnetic field in real time.

[0092] The verification logic of this device is as follows: First, the interaction between the DC and alternating magnetic fields in the superconducting tape will alter the non-uniform current density distribution along the width of the tape, thereby generating resistance. The measured voltage can then effectively verify the accuracy of the non-uniform current density distribution along the width of the superconducting tape obtained in the simulation.

[0093] Second, the resistance generated in the superconducting tape will cause a redistribution of DC current in the coil's circumferential and inter-turn branches, which will affect the coil voltage and magnetic field distribution. In particular, once the current changes from the circumferential branch to the inter-turn branch, it will no longer generate an axial magnetic field at the coil center. Measuring the axial magnetic field at the coil center can accurately reflect the redistribution of current in the coil in the circumferential and inter-turn branches.

[0094] Third, the redistribution of current in the circumferential branch and the inter-turn branch has a transient process, which causes the measured voltage and magnetic field to also have a transient process. The time constant of this transient process is related to the coil inductance and resistance. The accuracy of the inductance and resistance parameters in the simulation can be verified by measuring the transient process. Fourth, the axial alternating magnetic field component will induce additional induced current along the inter-turn contact in the coil. This induced current will shield the external alternating magnetic field. At this time, the measured voltage and magnetic field can well verify the current distribution obtained in the simulation.

[0095] Furthermore, applying an asymmetric magnetic field can induce three-dimensional effects in the coil. Compared to directly applying local thermal excitation, an asymmetric alternating external field is less likely to damage the coil and provides more subtle verification of the non-uniform current density distribution along the width direction inside the superconducting wire.

[0096] In summary, the present invention proposes a rapid three-dimensional electromagnetic simulation method and verification device for large-scale uninsulated coils. This method addresses key breakthroughs in existing three-dimensional simulation technologies for large-scale uninsulated coils, such as high computational load, difficulty in achieving uniformity, poor coupling convergence, and insufficient current distribution accuracy, filling a technological gap in rapid three-dimensional simulation of ultra-large uninsulated coils. The method balances modeling simplicity, computational efficiency, and simulation accuracy, and is complemented by a designed verification device to ensure the reliability of the simulation model.

[0097] From the perspective of improving computational speed, this invention has significant advantages. By homogenizing the process and blurring the boundaries between turns, it avoids modeling each turn, reduces the amount of computation, and greatly improves computational efficiency, meeting the needs of rapid simulation of large coils.

[0098] In terms of ease of modeling, this invention excels. It proposes a three-dimensional simulation method for large uninsulated coils based on a homogenized model, which equates multi-turn coils to a homogenized continuum model. This breaks through the limitations of traditional turn-by-turn modeling, significantly reducing modeling complexity. The accuracy of the simulation results in the radial direction can be increased simply by refining the mesh radially.

[0099] In terms of convergence, this invention also exhibits unique advantages. By abandoning the field-circuit coupling model, it fundamentally avoids problems such as coupling non-convergence, high-frequency fluctuations, and result distortion, providing a stable and reliable new model architecture for the simulation of large-scale uninsulated coils.

[0100] In terms of computational accuracy, compared to the field-circuit coupling model that divides the data into geometrically uniform units, this invention presents a geometrically uniform body, which makes the current distributed continuously rather than discretely along the radial direction. This results in higher current distribution resolution and is closer to the real physical scenario.

[0101] In terms of application scenario adaptability, this invention can be adapted to different types of large uninsulated coils, including closed-loop coils and open-loop coils, and can simulate complex working conditions, that is, it can consider non-uniform current density distribution in various dimensions, and has wide applicability and powerful functions.

[0102] Based on the verification results, the simulation model established by this invention has a fast calculation speed for large coils, minimal error compared with the benchmark model, small calculation error for three-dimensional spatial current distribution, improved stability of multi-physics coupling simulation, and high convergence rate of continuous iterative calculation, providing a highly reliable and accurate simulation method for the performance study of large uninsulated coils.

Claims

1. A rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils, characterized in that, Includes the following steps: Step 1: Establish the electromagnetic simulation control equations for the coil model. The coil model is a uniform geometric model, and the individual turns within the model are not distinguished. Step 2: Establish the equivalent theory, and based on the equivalent theory, establish the current source region and the inter-turn resistance region of the coil. The current source region is a sector cut off from the coil body, and the inter-turn resistance region is a geometric body that is free outside the coil body and connected in parallel with the current source region. Step 3: Based on the equivalent theory, anisotropic resistivity is set for the coil of the homogenized body. The resistivity in the circumferential and axial directions is set to the resistivity in the length and width directions of the conductor, respectively, and the resistivity in the radial inter-turn direction is set to complete insulation, i.e., infinite. Step 4: Apply the excitation conditions to the corresponding current source region according to whether the coil is open-loop or closed-loop. Step 5: Set the resistivity of the inter-turn resistance region based on the equivalent theory to equivalently simulate the inter-turn resistance of different sizes of uninsulated coils; Step 6: Conduct mesh generation and calculation accuracy verification, increase the radial mesh density and verify the convergence of simulation results as the radial mesh density increases. When the convergence meets the set requirements, the mesh generation accuracy is considered to have met the requirements.

2. The rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils according to claim 1, characterized in that, The electromagnetic simulation control equations in step 1 include, but are not limited to: （1）； In the formula, For the Laplace operator, The magnetic field strength, For electric field strength, For current density, For external current density, Permeability, is the resistivity.

3. The rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils according to claim 1, characterized in that, The equivalent theory in step 2 aims to establish a simulation model that can be uniform along the radial direction of the coil without dividing each turn; in order to establish the equivalent theory, a circuit theory model of an uninsulated coil is established. The circuit theory model is only used for the construction of the equivalent theory and equivalent process; the circuit theory model includes the wires of each turn of the coil, the inter-turn contact resistance between turns, and the current source connected to the end of the coil. The equivalent theory includes: Step 2.1: Concentrate and compress the inter-turn resistance of the uninsulated coil, which is distributed throughout the entire circumferential direction, to a certain circumferential position; Step 2.2: Cut off the connection between the Nth turn and the N+1th turn and reconnect it back to the Nth turn. On the node formed after reconnection, set the node current constraint according to whether the coil end is connected to a current source or directly short-circuited to form a closed loop. Step 2.3: After eliminating the series connection between turns along the length of the conductor in step 2.2, the coil, inter-turn resistance and node current source are homogenized radially to form a homogenized body. In the homogenized body, a certain area cut off from the coil sector is used as the current source area, and a solid area connected in parallel to the current source area and free from the coil body is constructed as the inter-turn resistance area. A model framework that can be established by a finite element field model is formed.

4. The rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils according to claim 3, characterized in that: In step 2.2, when each turn of the coil is cut and reconnected, for an open-loop coil with a current source connected to its end, an inserted current source is added to the reconnected node, and the current value of the inserted current source is equal to the current value of the current source at the end of the coil, and the current source connected to the end of the coil is removed; for a closed-loop coil with the end short-circuited to form a closed loop, the node current values ​​before and after reconnection are constrained to be equal, and the short-circuiting wire at the end of the coil is removed.

5. The rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils according to claim 3, characterized in that, The formation of the current source region in step 2.3 includes: in the case of an open-loop coil, the current sources added to the nodes are merged into a homogenized body along the radial direction to form a homogenized current source region; in the case of a closed-loop coil, nodes with equal constrained currents are merged into a homogenized body along the radial direction to form a homogenized region, and the current distribution of the merged homogenized region is constrained to be uniform and unchanged along the radial direction.

6. The rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils according to claim 2, characterized in that, The setting of anisotropic resistivity in step 3 satisfies: radial resistivity Resistivity set as insulation, circumferential resistivity Resistivity along the length of the conductor, axial resistivity The resistivity is denoted by ρ, which represents the resistivity along the height of the conductor. In high-temperature superconducting tapes, The resistivity is denoted as ρ_resistivity along the length of the strip. The resistivity is in the width direction of the strip; to achieve anisotropic resistivity, in formula (1) In the governing equations, E and J All are three-dimensional vectors.

7. The rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils according to claim 6, characterized in that, The requirement to satisfy the anisotropic resistivity setting The governing equations need to be transformed into Cartesian coordinates. The specific process and expression are as follows: （2）； （3）； （4）； In the formula, , , These represent the electric field strengths along the radial, circumferential, and axial directions of the coil, respectively. , , The current density is measured in the radial, circumferential, and axial directions of the coil. The angle between the length direction of the conductor and the y-axis of the Cartesian coordinate system; , , These are the components of the electric field intensity in the Cartesian coordinate system. , , These are the current density components in the Cartesian coordinate system.

8. The rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils according to claim 6, characterized in that: The setting of anisotropic resistivity in step 3 further includes, if there are arcs or curved edges in the coil, these regions must be modeled as polygons with straight edges; based on this, the conductor length direction vector within each sector of the polygon is constant, therefore, the resistivity in each sector is set... The angular variable is a constant that remains unchanged at each position in space, allowing even a first-order, single-grid design to accurately describe the region in each sector. Angular variables reduce the requirements for the mesh.

9. The rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils according to claim 1, characterized in that, In step 4, the excitation condition for the open-loop coil is: the current density in the constrained current source region is a constant value, and an external current density is applied. This allows the current source region to be equivalent to the current source connected to the coil ends, where... The expression is: （5）； In the formula, , , These represent the external current densities in the coil turns direction, circumferential direction, and axial direction, respectively. The current supplied to the current source; The cross-sectional area through which the circumferential current can flow in a single conductor is given; at the same time, the resistivity in all directions of the current source region is set to be the insulating resistivity to avoid the generation of additional interference current, so that the current density in the current region is equal to the set external current density, i.e., formula (5).

10. The rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils according to claim 1, characterized in that, The excitation condition for the closed-loop coil in step 4 is that the resistivity in all directions of the current source region is set to be the insulating resistivity, and the external current density is... for: （6）； In the formula, The total ampere-turns of the coil's circumferential current is calculated by selecting a cross-section of the coil through which the circumferential current flows and integrating the circumferential current density thereon. , The total ampere-turns of the inter-turn current is calculated by selecting a cross section in the inter-turn resistance region through which the circumferential current flows and integrating the circumferential current density on that section. , It is the cross-sectional area of ​​the coil that allows circumferential current to flow through.

11. The rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils according to claim 10, characterized in that, When the closed-loop coil has a multi-pane structure, the current source region of the coil... satisfy: （7）； In the formula, This represents the total number of coils contained in the coil. The serial number represents the thread.

12. The rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils according to claim 1, characterized in that, In step 5, the inter-turn resistance region needs to be set to anisotropic resistivity, wherein the radial resistivity of the inter-turn resistance region is... and axial resistivity Let the resistivity range of the insulating material be defined, and the circumferential resistivity be defined. Set as formula (8): （8）； In the formula, The contact resistance between individual turns. The circumferential length of the inter-turn resistance region; It is the cross-sectional area of ​​a single conductor that allows circumferential current to flow through.

13. The rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils according to claim 1, characterized in that: In step 6, the criteria for verifying the computational accuracy include: if the simulation results gradually converge to a fixed value as the mesh density increases, then the mesh accuracy is sufficient; if the simulation results still show a trend of a rate of change greater than the set value, then the mesh needs to be further refined.

14. A rapid three-dimensional electromagnetic simulation verification device for large-scale uninsulated coils, which is a device for verifying the rapid three-dimensional electromagnetic simulation method for large-scale uninsulated coils as described in any one of claims 1 to 13, characterized in that, include: Large uninsulated coils; Current source module, used to supply DC current to large uninsulated coils; The alternating external field application module uses an AC power supply connected to a magnet to apply alternating external fields of different directions, amplitudes, and frequencies; the measurement module includes a voltage measurement unit based on a nanovoltmeter and a magnetic field measurement unit based on a Hall probe and a gaussmeter; the device verifies the performance of the simulation model by applying an alternating magnetic field and measuring the coil voltage and magnetic field in real time by passing DC current through the device.

15. The large-scale uninsulated coil rapid three-dimensional electromagnetic simulation verification device according to claim 14, characterized in that, The performance logic of the verification simulation model includes: verifying the non-uniform current density distribution in the width direction of the superconducting tape by measuring voltage; verifying the circumferential and inter-turn current distribution by measuring voltage and magnetic field; verifying the time constant related to coil inductance and resistance by measuring the transient change process of magnetic field and voltage; and completing the verification by applying an asymmetric magnetic field to excite the three-dimensional eddy current effect of the coil.

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