Method and apparatus for calculating loss of tape joint of high temperature superconducting cable and superconducting coil

Abstract

This invention relates to a method and apparatus for calculating the loss of strip joints in high-temperature superconducting cables and superconducting coils, belonging to the field of strip joint loss measurement technology. The method includes: obtaining the structural parameters of a second-generation high-temperature superconducting strip; isolating and modeling the joint region, determining the expansion coefficient based on the inner radius of the strip, equating the joint length to the perimeter of the strip at the corresponding position, constructing a two-dimensional axisymmetric model of the joint region, and setting a coordinate transformation matrix based on the deflection of the current path; constructing a three-component resistivity matrix of the two-dimensional axisymmetric model based on the structural parameters of the second-generation high-temperature superconducting strip and the coordinate transformation matrix, calculating the resistivity component of the joint region, thereby obtaining the current density component of the joint region through the two-dimensional axisymmetric model; and calculating the power loss result of the joint region based on the resistivity and current density components of the joint region. Compared with the prior art, this invention achieves accurate calculation of the loss of a normal-conducting joint and adjacent regions.

Description

Technical Field

[0001] This invention relates to the field of strip joint loss measurement technology, and in particular to a method and apparatus for calculating strip joint loss of high-temperature superconducting cables and superconducting coils. Background Technology

[0002] In recent years, as the application of second-generation high-temperature superconducting tapes in power facilities has gradually moved towards industrialization, its connection technology, as one of the key technologies for the large-scale application of tapes, has begun to receive close attention. The main reasons are as follows: (1) At present, the production cost of long-distance, highly uniform superconducting tapes is very high. For power equipment with high wire demand, the use of multiple connection methods has significant economic advantages. (2) During the winding process of cables and magnet coils, due to the limitations of current carrying capacity, voltage impedance and cooling devices, it is necessary to make connection treatment between cables and cables, and between coils.

[0003] Currently, the connection technology of second-generation high-temperature superconducting tapes can be divided into the following two types: (1) Normal conduction connection: that is, after connection, the superconducting tape has a certain resistance in the joint area during current carrying. Its value is generally related to the connection method, dielectric material and superconducting tape packaging method. At present, the more mature technologies are mechanical pressing method, silver diffusion method and brazing method. Among them, the brazing method is the most commonly used. (2) Superconducting connection: that is, the superconducting surfaces of two superconducting tapes are directly connected or superconducting materials are used as dielectrics for connection. Its resistance value can generally be as low as 10. -12 While the Ω value is below a certain threshold, the economic cost is very high, and the operating environment requirements are stringent. Therefore, considering factors such as the difficulty of the manufacturing process and the economics of application, brazing is often used in practical applications to connect second-generation high-temperature superconducting tapes for normal conduction.

[0004] Since the resistance of a normal-conducting joint is mainly affected by the solder, welding area, welding thickness, and welding method, selecting appropriate welding materials and following proper operating procedures can reduce the resistance of the joint area to below nΩ. However, the essence of brazing is to weld the superconducting strips to be joined together using welding materials, so the current path between the two strips is not continuous. Therefore, during current carrying, current transfer across layers will inevitably occur in the connection area of ​​the superconducting strips, making this area exhibit a high-resistivity state. Furthermore, the operating conditions of superconducting power devices are complex, and the strip connection itself exhibits a higher resistance state than other areas, making it easier for heat to accumulate in this area during current carrying, threatening the safe operation of the superconducting power device.

[0005] The operating state of superconducting power devices is not constant, and the complex electromagnetic conditions of their environment result in a complex spatiotemporal distribution of current within the superconducting tape. This makes it difficult to describe the losses during the dynamic process using a simple linear relationship, a situation exacerbated in regions containing constant-conducting joints. Furthermore, the slow quench propagation speed of second-generation high-temperature superconducting tapes makes them prone to localized temperature rises under the influence of dynamic losses, thus affecting thermal stability. Traditional joint loss calculation methods treat the joint region as a constant resistance, neglecting the impact of current movement across layers on the dynamic resistivity of the joint region, and failing to incorporate this effect into the loss calculation, resulting in low accuracy.

[0006] In summary, research on normally conducting joints mainly focuses on process optimization and reduction of normal operating resistance, with little consideration given to the nonlinear current-voltage characteristics of superconducting tapes and the dynamic impact of current transfer across turns on the joint resistance value. Furthermore, joint losses are not included in the tape loss calculation during current carrying, making it impossible to accurately calculate the losses of normally conducting joints and adjacent areas, thereby threatening the stable operation of superconducting power devices. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art, which cannot accurately calculate the loss of the normal conducting joint and adjacent areas, and to provide a method and apparatus for calculating the loss of the tape joint of high-temperature superconducting cables and superconducting coils.

[0008] The objective of this invention can be achieved through the following technical solutions:

[0009] A method for calculating the strip joint loss of high-temperature superconducting cables and superconducting coils includes the following steps:

[0010] Obtain the structural parameters of second-generation high-temperature superconducting tapes;

[0011] The joint region of the second-generation high-temperature superconducting tape is modeled in isolation. Based on the inner radius of the second-generation high-temperature superconducting tape, the expansion coefficient is determined. The joint length is equivalent to the perimeter of the tape at the corresponding position. A two-dimensional axisymmetric model of the joint region is constructed, and the coordinate transformation matrix is ​​set according to the deflection of the current path.

[0012] Based on the structural parameters and coordinate transformation matrix of the second-generation high-temperature superconducting tape, the three-component resistivity matrix of the two-dimensional axisymmetric model is constructed, the resistivity component of the joint region is calculated, and the current density component of the joint region is obtained through the two-dimensional axisymmetric model.

[0013] The power loss in the joint area is calculated based on the resistivity and current density components of the joint area.

[0014] Furthermore, the structural parameters of the second-generation high-temperature superconducting tape include: overall width, thickness of each layer, length of the joint area, and thickness of the weld layer.

[0015] Furthermore, the isolated modeling of the junction region of the second-generation high-temperature superconducting tape includes constructing an equivalent uninsulated coil based on the inner radius of the second-generation high-temperature superconducting tape, thereby constructing a two-dimensional axisymmetric model of the junction region, and determining the expansion coefficient of the two-dimensional axisymmetric model of the junction region compared to the perimeter of the corresponding position of the second-generation high-temperature superconducting tape. γ The expansion coefficient γ The calculation expression is:

[0016]

[0017] In the formula, L J The total length of the joint area. R ci For the joint area corresponding to the first i The inner radius of the strip.

[0018] Furthermore, the calculation expression for the three-component resistivity matrix is ​​as follows:

[0019]

[0020] In the formula, The overall resistivity matrix of the joint region. ρ ct and ρ sc These are the radial resistivity components considering the resistivity of the joint region and the components considering the second-generation high-temperature superconducting tape, respectively. EJ The resistivity component of the superconducting layer. This is the coordinate transformation matrix. The coordinates are the three components of the actual coil structure. This represents the axial resistivity component.

[0021] Furthermore, the calculation expressions for the radial resistivity component and the superconducting layer resistivity component are as follows:

[0022]

[0023] In the formula, E c These are the critical electric field parameters for superconducting tapes; J τ This represents the current density component along the strip winding direction. J c For the critical current density function of second-generation high-temperature superconducting tapes; n The parameter values ​​reflect the diamagnetism of high-temperature superconducting tapes under varying magnetic fields;R ct This represents the total inter-turn contact resistance.

[0024] Furthermore, the total inter-turn contact resistance R ct The total inter-turn contact resistivity is calculated based on the ratio of strip length to cross-sectional area. The expression for calculating the total inter-turn contact resistivity is as follows:

[0025]

[0026] In the formula, The total inter-turn contact resistivity. This refers to the width of the second-generation high-temperature superconducting tape. ρ i The resistivity of each layer inside the second-generation high-temperature superconducting tape, excluding the superconducting layer. i =1- k , d i The thickness of each layer inside the second-generation high-temperature superconducting tape, excluding the superconducting layer. The resistivity of the welding material, The length of the weld layer. For the thickness of the weld layer, The thickness is that of the second-generation high-temperature superconducting tape.

[0027] Furthermore, the coordinate transformation matrix The calculation expression is:

[0028]

[0029] In the formula, α The rotation deflection angle of the region to be transformed;

[0030] The rotation deflection angle α The calculation expression is:

[0031]

[0032] In the formula, d The thickness of the superconducting tape. These are the radial coordinates of the region to be transformed in cylindrical coordinates.

[0033] Furthermore, the calculation expression for the power loss result in the joint area is as follows:

[0034]

[0035] In the formula, For power loss in the connector area, The total loss of the superconducting layer in the two-dimensional axisymmetric model is obtained based on the current density components and superconducting layer resistivity along the winding direction of the second-generation high-temperature superconducting tape. The loss of the inter-turn contact layer in the two-dimensional axisymmetric model is obtained based on the current density component and radial resistivity perpendicular to the surface of the second-generation high-temperature superconducting tape.

[0036] Furthermore, the method is applicable to the calculation of strip joint losses for bridging joints, stacked strips, and cables.

[0037] The present invention also provides a device for calculating the strip joint loss of high-temperature superconducting cables and superconducting coils, including a memory and a processor. The memory stores a computer program, and the processor calls the computer program to execute the steps of the method described above.

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] (1) This invention proposes a method for calculating the joint loss of second-generation high-temperature superconducting tape based on finite element simulation. By establishing a finite element model of second-generation high-temperature superconducting tape containing a normal conducting joint, the current distribution of the joint and the surrounding area is simulated to obtain key parameters such as resistivity, electric field, and magnetic field in the corresponding area. Then, the total loss of the joint area is calculated, providing reliable data support for the dynamic stability evaluation of large-scale superconducting power devices such as long-distance superconducting cables and large-capacity superconducting magnets.

[0040] (2) The present invention takes into account that the actual structure of the joint region of the second-generation high-temperature superconducting tape is relatively complex. If the corresponding actual geometric model is directly established during modeling, it is difficult to solve the subsequent problem. The current distribution inside the joint region is mainly affected by its own current carrying capacity and spatial magnetic field, and is not related to the current distribution of the tape in the adjacent region. Therefore, the joint region is isolated and modeled to effectively reduce the complexity of the model. The equivalent model of the joint length is performed according to the inner radius of the tape corresponding to the joint region, and the corresponding expansion coefficient is determined to adjust the joint loss calculated later. This realizes the accurate and reliable simplified modeling of the joint region model.

[0041] (3) In the process of calculating the resistivity parameters inside the coil, the present invention takes into account the deflection of the current path inside the two-dimensional axisymmetric model and the current path in the actual model. Therefore, taking into account the thickness of the high-temperature superconducting tape and the winding deflection angle, a coordinate transformation matrix is ​​constructed to compensate for the deflection of the current path and improve the accuracy of the subsequent calculation results.

[0042] (4) The present invention calculates the joint loss by considering the total loss of the superconducting layer and the inter-turn contact layer loss in the two-dimensional axisymmetric model, and combines the corresponding expansion coefficient, so that the joint loss result obtained is more accurate and reliable. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating a method for calculating the strip joint loss of a high-temperature superconducting cable and superconducting coil provided in an embodiment of the present invention.

[0044] Figure 2 This is a schematic diagram of a layered structure of a second-generation high-temperature superconducting tape provided in an embodiment of the present invention;

[0045] Figure 3 The following are schematic diagrams of three joint structures provided in the embodiments of the present invention, wherein (a) is a lap joint, (b) is a butt joint, and (c) is a bridge joint;

[0046] Figure 4 The present invention provides an equivalent process for a joint area, taking a CORC cable as an example, wherein (a) is a CORC cable with a joint, (b) is a single strip joint after area extraction, (c) is a simplified ring structure of the joint, and (d) is an expansion model after bidirectional expansion.

[0047] Figure 5 This is a schematic diagram of equivalent area comparison provided in an embodiment of the present invention, wherein the dashed line is the single strip joint after extraction and expansion, and the orange shaded area is the strip area generated by expansion;

[0048] Figure 6 This is a schematic diagram of coordinate transformation corresponding to a model transformation provided in an embodiment of the present invention, wherein (a) is the original three-dimensional coordinates of the high-temperature superconducting tape, (b) is the three-dimensional coordinates of the high-temperature superconducting tape after coordinate rotation based on the rotation deflection angle, and (c) is the correspondence before and after coordinate rotation.

[0049] Figure 7 This is a schematic diagram of inter-turn loss during the excitation process provided in Embodiment 1 of the present invention;

[0050] Figure 8 This is a schematic diagram of superconducting layer loss during the excitation process provided in Embodiment 1 of the present invention;

[0051] Figure 9 This is a schematic diagram of an equivalent process in a joint area provided in an embodiment of the present invention;

[0052] Figure 10 This is a schematic diagram of inter-turn loss during the excitation process provided in Embodiment 2 of the present invention;

[0053] Figure 11 This is a schematic diagram of superconducting layer loss during the excitation process provided in Embodiment 2 of the present invention. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0055] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0056] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0057] Example 1

[0058] like Figure 1 As shown, this embodiment provides a method for calculating the strip joint loss of high-temperature superconducting cables and superconducting coils, including the following steps:

[0059] S1: Obtain the structural parameters of the second-generation high-temperature superconducting tape;

[0060] Specifically, key parameters such as the width of the second-generation high-temperature superconducting tape, the thickness of each layer, the length of the joint area, and the thickness of the weld layer were obtained.

[0061] like Figure 2 As shown, the second-generation high-temperature superconducting tape has a layered composite structure. Due to the influence of the production process and whether it is encapsulated, the width, thickness of each layer and number of layers of the second-generation high-temperature superconducting tape vary from manufacturer to manufacturer. Therefore, it is necessary to make adjustments according to the actual situation.

[0062] Welded joints can be classified into butt joints, lap joints, and bridging joints. Figure 3Three types of joint structures are shown in the diagram. The lap joint has a larger contact area, and it's relatively easy to apply pressure perpendicular to the surface of the strip during joint fabrication. Therefore, the lap joint has very low resistance and the highest technological maturity, making it suitable for large power installations such as cables and magnets. The butt joint has a simpler structure and is generally used for internal coils in uniform magnets where a smooth joint surface is required. However, due to its smaller effective contact area, the joint resistance is higher, making it unsuitable for the development needs of superconducting power devices. The bridging joint is generally used for connections between coils, where the two strips are on the same horizontal plane after welding. However, the bridging joint has a higher resistance than the lap joint and is generally used for coil-to-coil joint fabrication.

[0063] The resistance of welded joints in second-generation high-temperature superconducting tapes is affected by various factors, including the welding material, the thickness of the welded area, and the joint length. Generally, higher external pressure and higher welding temperature during welding promote more thorough contact between the solder and the second-generation high-temperature superconducting tape, filling the surface of the protective / encapsulation layer and effectively reducing the thickness of the weld layer, thereby lowering the joint resistance. However, excessive welding pressure or temperature can lead to structural losses in the superconducting layer, significantly increasing the joint resistance.

[0064] S2: The joint region of the second-generation high-temperature superconducting tape is isolated and modeled. Based on the inner radius of the second-generation high-temperature superconducting tape, the expansion coefficient is determined. The joint length is equivalent to the perimeter of the tape at the corresponding position. A two-dimensional axisymmetric model of the joint region is constructed, and the coordinate transformation matrix is ​​set according to the deflection of the current path.

[0065] S3: Based on the structural parameters and coordinate transformation matrix of the second-generation high-temperature superconducting tape, a three-component resistivity matrix of a two-dimensional axisymmetric model is constructed, and the resistivity component of the joint region is calculated. Thus, the current density component of the joint region is obtained through the two-dimensional axisymmetric model.

[0066] That is, the actual structure of the joint area is equivalent to the simplified geometric structure required to solve the model, and further equivalent to a two-dimensional axisymmetric model. At the same time, corresponding physical parameters are applied to each region in the finite element model.

[0067] The actual structure of the joint region is quite complex. Directly establishing a corresponding geometric model during modeling makes subsequent solutions difficult. Therefore, necessary simplifications and equivalences are required for the geometric model. Superconducting tapes in cables or coils generally require an insulating layer. Therefore, regardless of whether in steady-state or transient processes, there is no inter-turn current between the tapes; instead, current flows naturally along the winding path of the superconducting tape. At this time, only the current component along the tape winding direction exists inside the coil. For the joint region, the direct contact between the tapes provides a path for inter-turn current transfer. That is, in the joint region, components along the tape winding direction and perpendicular to the tape direction will exist simultaneously.

[0068] The current distribution within the joint area is primarily influenced by its own current-carrying capacity and the spatial magnetic field, and is independent of the current distribution in adjacent strip areas. Therefore, the joint area can be modeled in isolation to effectively reduce model complexity. Furthermore, solder exists between the strips within the joint; thus, during current transfer across turns, the integral of the current perpendicular to the strip surface in this area equals the circumferential current of the entire coil / cable (considering only a single layer of strip; for stacked strips, it is the sum of the currents of the stacked strips):

[0069] (1)

[0070] In the formula, ds Let the area of ​​the welding region be a micro-element. J n The current density component is perpendicular to the high-temperature superconducting tape. I op This refers to the operating current of the coil / cable.

[0071] Although the strip length required for welding generally does not exceed the circumference of the circle corresponding to its radius, in order to effectively simplify the model and accurately reflect the cross-turn transfer characteristics of the current in a two-dimensional axisymmetric model, the joint length needs to be equivalent to the circumference of the strip at the corresponding position. In this case, the expansion coefficient can be... γ Defined as:

[0072] (2)

[0073] In the formula L J The total length of the joint area. R ci For the joint area corresponding to the first i The inner radius of the strip. Figure 4 An equivalent process for the joint area using CORC cable as an example is given.

[0074] After expanding the joint area, the contact area of ​​the entire welding area is increased. γ The simulation model's joint area is 1 / 3 of the actual joint area. γ times, such as Figure 5 As shown. Since this model is a two-dimensional axisymmetric model, the current component values ​​of each region are equal throughout the entire contact surface. Therefore, if the operating current of this region is still set to... I op Then, the actual current density component perpendicular to the superconducting tape within the joint region should be equal to the simulation calculation result. γ times.

[0075] The inter-turn current in the joint area, i.e., the current density component perpendicular to the strip surface, is less affected by the spatial magnetic field. Therefore, after simplification and equivalence, the joint area can be regarded as a strip with 2 turns and an inner radius of... R ci The equivalent uninsulated coil, for k Cables / coils with two turns of strip wound together can be used in a single winding with two turns. k An equivalent model of an uninsulated coil is performed.

[0076] The constitutive equations of the equivalent uninsulated coil region can be reduced to Maxwell's equations in the two-dimensional axisymmetric case. At this point, only the resistivity parameters inside the coil need to be set, and the current distribution inside the coil can be obtained through Ohm's law and Ampere's law. However, the current path inside the two-dimensional axisymmetric model is deflected from the current path in the actual model. Therefore, it is necessary to transform the coordinate system of the simulation model so that its internal physical parameters and the subsequent calculated current results conform to the actual situation.

[0077] like Figure 6 As shown, considering both the thickness of the high-temperature superconducting tape and the winding deflection angle, the coordinate transformation matrix can be expressed as:

[0078] (3)

[0079] In the formula, α The rotational deflection angle can be defined as:

[0080] (4)

[0081] In the formula, These are the radial coordinates of the region to be transformed in cylindrical coordinates.

[0082] In the formula, d Let be the thickness of the superconducting tape. Then, the three-component resistivity matrix in the simulation model can be defined as:

[0083] (5)

[0084] In the formula, For the axial resistivity component, ρ ct and ρ sc These are respectively considering the radial resistivity component of the joint region resistivity and considering the second-generation high-temperature superconducting tape. EJ The resistivity components of the superconducting layer can be defined as follows:

[0085] (6)

[0086] In the formula, Ec This is the critical electric field parameter for superconducting tapes, typically set to 1µV / cm; J τ This represents the current density component along the strip winding direction. J c The critical current density function of the second-generation high-temperature superconducting tape can be set as the independent variable, such as magnetic field, temperature field and strain field, according to the physical field coupling relationship. n The parameter values ​​reflect the diamagnetism of high-temperature superconducting tapes under varying magnetic fields; R ct The total inter-turn contact resistance is defined as:

[0087] (7)

[0088] In the formula h tape This refers to the width of the second-generation high-temperature superconducting tape. ρ i ( i =1- k ( ) represents the resistivity of each layer inside the superconducting tape, excluding the superconducting layer. d i ( i =1- k ) represents the thickness of each layer inside the superconducting tape, excluding the superconducting layer; The resistivity of the welding material, This represents the length of the weld layer.

[0089] S4: Calculate the power loss result of the joint area based on the current density component of the joint area.

[0090] Joint loss can be expressed as:

[0091] (8)

[0092] In the formula, the total loss of the superconducting layer in the simulation model is... P sc (Mainly composed of the current density component along the winding direction of the superconducting tape) J τ (and the dynamic superconducting layer resistivity) is the actual superconducting layer loss in the joint region. γ The inter-turn contact layer loss is several times higher. P ct (Mainly composed of current density components perpendicular to the strip surface) J n (and radial resistivity) is the actual inter-turn loss in the joint area. γ One-third.

[0093] For structures such as bridging joints, stacked strips, and cables, they can also be transformed into similar double-turn coils, multi-turn coils, and layered coil structures, thereby enabling rapid calculation of joint losses.

[0094] This embodiment takes a single-layer three-strand parallel-wound CORC cable with lap joints as an example to calculate the joint loss during its operation. Table 1 gives the detailed parameters of the CORC cable and the second-generation high-temperature superconducting tape for calculating the joint loss.

[0095] Table 1 Simulation Parameters

[0096]

[0097] Assume the maximum operating current of a single strip in a CORC cable is 180A, and the current rise rate during excitation is 10A / s. During this process, the inter-turn layer loss in the CORC cable joint area is as follows: Figure 7 As shown. The main loss of the tape during excitation is the Joule loss generated by the current transfer across turns, and this loss does not decay to zero after the excitation process ends, but gradually tends to a constant value, which is 104mW in this embodiment. For the cable, this loss will continue to exist as a heat source during stable operation, so it needs to be taken into account in thermal stability analysis; since the superconducting tape is in a changing magnetic and electric field, a certain amount of AC loss will be generated at this time (mainly hysteresis loss in this embodiment), and this part of the loss will quickly decay to zero after the excitation process ends, and the maximum value of the loss during the excitation process is about 28mW, which accounts for a very small proportion of the total loss in the entire joint area, such as Figure 8 As shown.

[0098] Example 2

[0099] This embodiment takes a coil with lap joints as an example and calculates the joint loss during its operation separately. Table 2 provides detailed parameters of the second-generation high-temperature superconducting coil and the tape used for calculating the joint loss. Figure 9 The equivalent processing procedure for coil connectors is given, where L1 is the length of the innermost local connector area of ​​the lap joint, and L2 is the length of the single strip of the innermost lap joint. Compared with the CORC cable in Example 1, the processing procedure for coil connectors is simpler.

[0100] Table 2 Simulation Parameters

[0101]

[0102] Assuming the maximum operating current of the coil is 50A, and the current rise rate during excitation is 2.5A / s, the inter-turn layer loss in the junction area during this process is as follows: Figure 10As shown. Consistent with the joint loss calculation results of the CORC cable in Example 1, the main loss in the joint area during excitation is the Joule loss caused by current transfer across turns. In this example, the maximum loss during excitation is 100mW, and the steady-state value is 88mW.

[0103] In this embodiment, the peak AC loss is approximately 10mW, which is also a very small percentage of the total loss in the entire joint area. Furthermore, it rapidly decays to zero after excitation ends. The loss variation curve for the entire process is shown below. Figure 11 As shown.

[0104] Example 3

[0105] This embodiment provides a device for calculating the strip joint loss of high-temperature superconducting cables and superconducting coils, including a memory and a processor. The memory stores a computer program, and the processor calls the computer program to execute the steps of the method as described in Embodiment 1.

[0106] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0107] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0108] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0109] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0110] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0111] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for calculating the strip joint loss of high-temperature superconducting cables and superconducting coils, characterized in that, Includes the following steps: Obtain the structural parameters of second-generation high-temperature superconducting tapes; The joint region of the second-generation high-temperature superconducting tape is modeled in isolation. Based on the inner radius of the second-generation high-temperature superconducting tape, the expansion coefficient is determined. The joint length is equivalent to the perimeter of the tape at the corresponding position. A two-dimensional axisymmetric model of the joint region is constructed, and the coordinate transformation matrix is ​​set according to the deflection of the current path. Based on the structural parameters and coordinate transformation matrix of the second-generation high-temperature superconducting tape, the three-component resistivity matrix of the two-dimensional axisymmetric model is constructed, the resistivity component of the joint region is calculated, and the current density component of the joint region is obtained through the two-dimensional axisymmetric model. The power loss in the joint area is calculated based on the resistivity and current density components of the joint area.

2. The method for calculating the strip joint loss of a high-temperature superconducting cable and superconducting coil according to claim 1, characterized in that, The structural parameters of the second-generation high-temperature superconducting tape include: overall width, thickness of each layer, length of the joint area, and thickness of the weld layer.

3. The method for calculating the strip joint loss of a high-temperature superconducting cable and superconducting coil according to claim 1, characterized in that, The isolated modeling of the junction region of the second-generation high-temperature superconducting tape includes constructing an equivalent uninsulated coil based on the inner radius of the second-generation high-temperature superconducting tape, thereby constructing a two-dimensional axisymmetric model of the junction region, and determining the expansion coefficient of the two-dimensional axisymmetric model of the junction region relative to the perimeter of the corresponding position of the second-generation high-temperature superconducting tape. γ The expansion coefficient γ The calculation expression is: In the formula, L J The total length of the joint area. R ci For the joint area corresponding to the first i The inner radius of the strip.

4. The method for calculating the strip joint loss of a high-temperature superconducting cable and superconducting coil according to claim 1, characterized in that, The expression for calculating the three-component resistivity matrix is ​​as follows: In the formula, The overall resistivity of the joint area. ρ ct and ρ sc These are the radial resistivity components considering the resistivity of the joint region and the components considering the second-generation high-temperature superconducting tape, respectively. EJ The resistivity component of the superconducting layer. This is the coordinate transformation matrix. The three-component coordinates are shown for the actual structure of a second-generation high-temperature superconducting tape coil. This represents the axial resistivity component.

5. The method for calculating the strip joint loss of a high-temperature superconducting cable and superconducting coil according to claim 4, characterized in that, The calculation expressions for the radial resistivity component and the superconducting layer resistivity component are as follows: In the formula, E c These are the critical electric field parameters for superconducting tapes; J τ This represents the current density component along the strip winding direction. J c For the critical current density function of second-generation high-temperature superconducting tapes; n The parameter values ​​reflect the diamagnetism of high-temperature superconducting tapes under varying magnetic fields; R ct This is the total inter-turn contact resistance. The thickness is that of the second-generation high-temperature superconducting tape.

6. The method for calculating the strip joint loss of a high-temperature superconducting cable and superconducting coil according to claim 5, characterized in that, The total inter-turn contact resistance R ct The total inter-turn contact resistivity is calculated based on the ratio of strip length to cross-sectional area. The expression for calculating the total inter-turn contact resistivity is as follows: In the formula, The total inter-turn contact resistivity. This refers to the width of the second-generation high-temperature superconducting tape. ρ i The resistivity of each layer inside the second-generation high-temperature superconducting tape, excluding the superconducting layer. i =1- k , d i The thickness of each layer inside the second-generation high-temperature superconducting tape, excluding the superconducting layer. The resistivity of the welding material, The length of the weld layer. This refers to the thickness of the weld layer.

7. The method for calculating the strip joint loss of a high-temperature superconducting cable and superconducting coil according to claim 4, characterized in that, The coordinate transformation matrix The calculation expression is: In the formula, α The rotation deflection angle of the region to be transformed; The rotation deflection angle α The calculation expression is: In the formula, d The thickness of the superconducting tape. These are the radial coordinates of the region to be transformed in cylindrical coordinates.

8. The method for calculating the strip joint loss of a high-temperature superconducting cable and superconducting coil according to claim 1, characterized in that, The calculation expression for the power loss in the joint area is as follows: In the formula, For power loss in the connector area, The total loss of the superconducting layer in the two-dimensional axisymmetric model is obtained based on the current density components and superconducting layer resistivity along the winding direction of the second-generation high-temperature superconducting tape. The loss of the inter-turn contact layer in the two-dimensional axisymmetric model is obtained based on the current density component perpendicular to the surface of the second-generation high-temperature superconducting tape and the radial resistivity. γ This is the expansion coefficient.

9. The method for calculating the strip joint loss of a high-temperature superconducting cable and superconducting coil according to claim 1, characterized in that, The method is applicable to the calculation of strip joint losses for bridging joints, stacked strips, and cables.

10. A device for calculating the strip joint loss of high-temperature superconducting cables and superconducting coils, characterized in that, It includes a memory and a processor, the memory storing a computer program, and the processor calling the computer program to perform the steps of the method as described in any one of claims 1 to 9.

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