Method for calculating critical current and ac loss of high-temperature superconducting generator coil
The critical current and losses of the high-temperature superconducting generator coil were calculated using the J-model and direct coupling method. Combined with rotating domain switching technology, the problems of low computational efficiency and large error in the existing technology were solved, and high-precision coil performance evaluation and optimization design were achieved.
Patent Information
- Application Number
- CN202610358828.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-23
- Publication Date
- 2026-07-07
AI Technical Summary
Existing technologies suffer from low efficiency and large errors in calculating the critical current and AC loss of high-temperature superconducting generator coils, especially in the design of large-turn coils. Traditional methods require multiple iterations and simplified boundary conditions, resulting in large calculation errors.
The critical current is calculated using the J model. A two-dimensional axisymmetric model is established by combining the direct coupling method and the rotating domain exchange technique. The electromagnetic properties of the superconductor are described by the EJ power law and the Kim model. The current density dynamic equation is constructed. The stator coil loss is calculated by the direct coupling method, and the rotor coil loss is calculated by the rotating domain exchange technique.
It significantly improves computational efficiency and accuracy, reduces simulation time, ensures accurate assessment of rotor losses in narrow air gap and multi-turn coil designs, and avoids errors caused by simplified boundary conditions.
Smart Images
Figure CN122347003A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of superconducting technology, specifically relating to a method for accurately calculating the critical current and AC loss of a high-temperature superconducting generator coil. Background Technology
[0002] High-temperature superconducting (HTS) generators, due to their high critical current and low loss characteristics, are considered a key technology for next-generation aerospace power generation systems in the trend towards multi-electrification and hybrid electrification in aviation. The HTS coil is the core component of the superconducting motor, and its critical current assessment is crucial for ensuring the motor's superconducting operation. Furthermore, HTS coils experience electromagnetic energy loss, or AC loss, when operating under alternating magnetic fields or transmitting alternating current. Accurate calculation of the AC loss of HTS coils provides crucial information for superconducting material selection, winding structure design, and cooling system configuration.
[0003] Current technologies still have shortcomings in the study of critical current and AC losses of HTS coils. Regarding critical current assessment, traditional methods such as the H-model, based on finite element analysis, require simulating both the air and superconducting domains and necessitate multiple iterations, resulting in low efficiency for coils with large turns. In calculating AC losses, previous calculations often simplified boundary conditions and neglected rotor losses; however, in motor designs with small air gaps and numerous rotor coil turns, this simplification introduces significant errors. Therefore, a method that can accurately and efficiently assess the critical current and AC losses of HTS coils is urgently needed. Summary of the Invention
[0004] To overcome the shortcomings of existing technologies, this invention provides a precise method for calculating the critical current and AC losses of high-temperature superconducting generator coils. Based on the J-model, the critical current is calculated, significantly improving computational efficiency. To address the problem of large calculation errors in AC losses of high-temperature superconducting coils, this invention employs a direct coupling method without simplifying boundary conditions, improving the accuracy of stator coil AC loss calculation. To solve the problems of long simulation time and difficult convergence in rotor AC loss calculation, this invention proposes a technique called rotating domain exchange, which enables accurate calculation of rotor AC losses in a real dynamic electromagnetic environment. Calculation results confirm that in high-temperature superconducting generators with small air gap widths and a large number of rotor coil turns, rotor coil AC losses are not negligible. The promotion of this invention is of great significance for the performance evaluation and optimization design of high-temperature superconducting generator coils.
[0005] The technical solution adopted by this invention to solve its technical problem is as follows: Step 1: Establish a two-dimensional axisymmetric model of the HTS coil; Step 2: Describe the electromagnetic properties of the superconductor; Step 3: Establish the current density dynamic equation based on the J model; Step 4: Calculate the voltage and critical current; Step 5: After calculating the critical current of the HTS coil, further evaluate its AC losses; Step 6: Construct a numerical model based on the TA model to provide a theoretical framework for subsequent loss calculations; Step 7: Calculate the AC loss of the stator coil using the direct coupling method; Step 8: Calculate the AC loss of the rotor coil using the rotating domain exchange technique.
[0006] Preferably, step 1 specifically comprises: The three-dimensional HTS coil is simplified into a two-dimensional axisymmetric coil model. In the modeling process, only the superconducting layer is considered, other material layers are ignored, and only the superconducting coil body is modeled, ignoring the air domain to simplify the calculation.
[0007] Preferably, step 2 specifically comprises: HTS coil electric field strength The EJ power-law relationship shown in equation (1) determines that, For the critical electric field, The loss index; For depends on magnetic flux density The critical current density is calculated using the Kim model shown in equation (2), where, , and These are parameters belonging to the Kim model, used to describe the anisotropy of high-temperature superconducting tapes; magnetic field components parallel to the tape surface. and magnetic field components perpendicular to the strip surface Determined by the Biot-Savart law; (1) (2).
[0008] Preferably, step 3 specifically comprises: In the J model, current density The current density is directly used as the state variable to be determined. A dynamic equation for the current density is established through integration, and the expression for the desired quantity is derived. For the two-dimensional axisymmetric coil model, the high-temperature superconductor region... Total magnetic vector potential Represented by equation (3), this formula shows It has two components, where, It is caused by the applied magnetic field. The generated vector potential With the current used to drive transmission Applying an electric field The generated vector potential The sum of these is an externality; The magnetic vector potential is generated by the interaction between currents and belongs to the internal interaction; then, by using Maxwell's equations, EJ power law and Kim model, the current density dynamic equation of the coil model is established, as shown in equation (4), where The vacuum permeability; It is a two-dimensional integral kernel generated using the geometric relationships of the model and the established cylindrical coordinate system; Calculated according to the law of electromagnetic induction It is the quantity to be solved, representing the first... The magnitude of the electric field strength of each coil; Represents the area differential element in two-dimensional space. This represents the integration variable, and other points in space. This indicates the location of the field point to be solved. It is the core state variable of the J model, representing the time-varying current density distribution in the superconducting coil; The time-varying component of the applied magnetic field in the x-direction. The component of the applied magnetic field in the y-direction that varies with time; (3) (4).
[0009] Preferably, step 4 specifically comprises: Based on the current constraint condition shown in equation (5), we obtain the following about The system of linear equations is shown in equation (6); where and Calculated from equations (7) and (8), It is the element in the i-th row and j-th column of a matrix, used to describe the coupling relationship between the turns of the superconducting coil. Let represent the equivalent driving source in the j-th turn of the coil, i.e., the total excitation source driving the electric field of the j-th turn of the coil; the electric field of the high-temperature superconducting coil under arbitrary transmission current is calculated according to equation (6). Furthermore, the average voltage of the coil under any transmission current is obtained, and the critical current of the coil is determined by combining the critical current criterion of 1 μV / cm. (5) (6) (7) (8) in, This represents the equivalent electric field in superconducting materials.
[0010] Preferably, step 5 specifically comprises: First, based on the structural parameters of the HTS motor, a 2D electromagnetic simulation model was constructed using finite element simulation software, including the stator, rotor, air gap, and aluminum barrel shielding structure. The specific settings are as follows: Motor structural parameters: The motor selected in this invention is an 8-pole, 12-slot synchronous generator. The stator adopts a 12-slot structure, and the rotor adopts an 8-pole built-in structure with an air gap width of 5mm. Both the stator and rotor coils are racetrack-shaped coils wound with YBCO superconducting tape. The stator armature winding consists of 12 double-racetrack coils, each with 12 turns. The rotor excitation winding consists of 8 racetrack coil assemblies, each assembly containing 5 racetrack coils, each coil with 60 turns. Material parameters: The stator and rotor cores are made of silicon steel sheet DW360_50, the width of YBCO strip is 4mm, the thickness of HTS layer is 1μm, and the critical current under 20K self-field is 1188A. The losses of the silver, copper, and Hastelloy layers in the YBCO strip are ignored, and only the AC losses of the HTS layer are calculated. The thickness of the HTS strip is ignored, and the 3D coil structure is simplified to a 2D model. Since the AC losses are mainly generated in the straight part of the coil, the curved part of the raceway coil is ignored. The total number of turns of the stator coil is 2×12, and the total number of turns of the rotor coil is 5×60.
[0011] Preferably, step 6 specifically comprises: Define the current density vector potential in the superconducting domain Used to solve for the current density of HTS coated conductors. The distribution is shown in equation (9); in the two-dimensional model, its boundary conditions are shown in equation (10), where, It is the vector potential of the current density on the width side of the strip; Let the vector potential of the current density on the other side be denoted as . ; The current flowing through a single HTS tape; the magnetic field vector potential is defined in both the superconducting and non-superconducting domains. Its expression is shown in equation (11), where Permeability, Let be the electrical conductivity, and let the boundary conditions be the magnetic field vector potential. ; For vector differentiation, denote the curl operation; (9) (10) (11).
[0012] Preferably, step 7 specifically comprises: The direct coupling method involves directly selecting the coil domain from the HTS generator model to establish the coil model. In the COMSOL simulation software, the coupling model is constructed using the coefficient-form boundary partial differential equation CB and the rotating machinery magnetic interface RMM. Based on the EJ power law, Kim model, and TA model, the current density distribution of the stator coils is calculated by performing calculations on each turn of each stator coil. Integrate to obtain the instantaneous AC loss of the stator coil, and average it over time to obtain the total AC loss of the stator.
[0013] Preferably, step 8 specifically comprises: Using a direct coupling method, the electromagnetic model of the rotor coil is constructed through the CB interface of the coefficient-form boundary partial differential equations. Material parameters and boundary conditions in formulas (10) and (11) are substituted. Based on the EJ power law, Kim model, and TA model, the current density distribution of the rotor coil is calculated. Integrating the instantaneous AC loss yields the total AC loss of the rotor, which is then averaged over time.
[0014] Preferably, the superconducting layer has a width of 4 mm and a thickness of 1 mm.
[0015] The beneficial effects of this invention are as follows: This invention employs the J-model to calculate the critical current, significantly improving computational efficiency compared to the traditional H-model. A direct coupling method is used to calculate coil AC losses, eliminating the need to simplify electromagnetic field boundaries and reducing estimation errors. The rotating domain exchange technique solves the convergence problem in rotor coil rotation simulation, avoiding the need for simulation of complex coil structures and significantly shortening simulation time. Calculation results confirm that rotor AC losses in narrow-gap, multi-turn superconducting motors are not negligible and should be carefully estimated or optimized. Attached Figure Description
[0016] Figure 1 This is a two-dimensional axisymmetric model diagram of an HTS coil.
[0017] Figure 2 This is a structural diagram of the stator and rotor coils.
[0018] Figure 3 This is a current density distribution diagram of the stator coil at 10ms.
[0019] Figure 4 This refers to the instantaneous AC loss of the stator coil.
[0020] Figure 5 This is a schematic diagram of the rotating domain for calculating stator AC losses and rotor AC losses.
[0021] Figure 6 This is a current density distribution diagram of the rotor coil at 20ms.
[0022] Figure 7 This represents the instantaneous AC loss of the rotor coil. Detailed Implementation
[0023] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0024] This invention proposes a critical current calculation method based on the J-model, significantly improving computational efficiency. To address the problem of large calculation errors in AC losses, this invention employs a direct coupling method without simplifying boundary conditions to improve the accuracy of stator coil AC loss calculation. To address the difficulty of simulation modeling caused by rotor rotation, a technique called rotation domain exchange is proposed. This technique enables accurate calculation of rotor AC losses in a real dynamic electromagnetic environment. The technical solution is as follows: Step 1: Establish a two-dimensional axisymmetric model of the HTS coil. To improve computational efficiency, the three-dimensional HTS coil is simplified into a two-dimensional axisymmetric coil model. During the modeling process, only the superconducting layer with a width of 4 mm and a thickness of 1 mm is considered; other material layers are ignored, and only the superconducting coil body is modeled, ignoring the air domain to simplify the calculation.
[0025] Step 2: Description of the electromagnetic properties of the superconductor. Electric field strength of the HTS coil. The EJ power-law relationship shown in equation (1) determines that, For the critical electric field, This is the loss index. For depends on magnetic flux density The critical current density can be calculated using the Kim model shown in equation (2). , and These are parameters belonging to the Kim model, used to describe the anisotropy of high-temperature superconducting tapes. They represent the magnetic field components parallel to the tape surface. and magnetic field components perpendicular to the strip surface It can be determined by the Biot-Savart law.
[0026] (1) (2) Step 3: Establish the current density dynamic equation based on the J-model. In the J-model, the current density... The current density is directly used as the state variable to be determined. A dynamic equation for the current density is established through integration, and the expression for the desired quantity is derived. For the two-dimensional axisymmetric coil model, the high-temperature superconductor region... Total magnetic vector potential It can be expressed as equation (3), which shows that It has two components. Among them, It is caused by the applied magnetic field. The generated vector potential With the current used to drive transmission Applying an electric field The generated vector potential The sum of these is an externality. The magnetic vector potential is generated by the interaction between currents and belongs to the internal interaction. Then, by applying Maxwell's equations, EJ's power law, and the Kim model, the current density dynamic equation of the coil model can be established, as shown in equation (4). The vacuum permeability; It is a two-dimensional integral kernel generated using the geometric relationships of the model and the established cylindrical coordinate system; Calculated according to the law of electromagnetic induction, and It is the quantity to be solved, representing the first... The magnitude of the electric field strength of each coil.
[0027] (3) (4) Step 4: Calculate the voltage and critical current. Based on the current constraint condition shown in equation (5), the following can be obtained: The system of linear equations is shown in equation (6). and It can be calculated using equations (7) and (8). Based on the above equations, the electric field of the high-temperature superconducting coil under any transmission current can be calculated. Furthermore, the average voltage of the coil under any transmission current is obtained, and the critical current of the coil is determined by combining the critical current criterion of 1 μV / cm.
[0028] (5) (6) (7) (8) Step 5: After calculating the critical current of the HTS coil, further evaluate its AC losses. First, based on the structural parameters of the HTS motor, a 2D electromagnetic simulation model is constructed using finite element simulation software. The model includes the stator, rotor, air gap, and aluminum barrel shielding structure, with the specific settings as follows: Motor structural parameters: The motor selected in this invention is an 8-pole, 12-slot synchronous generator. The stator adopts a 12-slot structure, and the rotor adopts an 8-pole built-in structure with an air gap width of 5mm. Both the stator and rotor coils are racetrack-shaped coils wound with YBCO superconducting tape. The stator armature winding consists of 12 double-racetrack coils, each with 12 turns. The rotor excitation winding consists of 8 racetrack coil assemblies, each assembly containing 5 racetrack coils, each coil with 60 turns.
[0029] Material parameters: The stator and rotor cores are made of silicon steel sheet DW360_50, the width of YBCO strip is 4mm, the thickness of HTS layer is 1μm, and the critical current under 20K self-field is 1188A.
[0030] The losses of the silver, copper, and Hastelloy layers in the YBCO strip are ignored, and only the AC losses of the HTS layer are calculated. The thickness of the HTS strip is ignored, and the 3D coil structure is simplified to a 2D model. Since the AC losses mainly occur in the straight sections of the coil, the curved sections of the racetrack coil are ignored. The total number of turns in the stator coil is 2×12, and the total number of turns in the rotor coil is 5×60.
[0031] Step Six: Construct a numerical model based on the TA model to provide a theoretical framework for subsequent loss calculations. Define the current density vector potential in the superconducting domain. Used to solve for the current density of HTS coated conductors. The distribution is shown in equation (9). In the two-dimensional model, its boundary conditions are shown in equation (10). Wherein, It is the vector potential of the current density on the width side of the strip. Let the vector potential of the current density on the other side be denoted as . , Let be the current flowing through a single HTS tape. Define the magnetic field vector potential in both superconducting and non-superconducting domains. Its expression is shown in equation (11), where Permeability, Let be the electrical conductivity, and let the boundary conditions be the magnetic field vector potential. .
[0032] (9) (10) (11) Step 7: Calculate the AC losses of the stator coils using the direct coupling method to avoid boundary simplification errors. The direct coupling method involves directly selecting the coil domain from the HTS generator model to establish the coil model. In COMSOL simulation software, the coupled model is constructed using coefficient-form boundary partial differential equations (CB) and rotating machinery magnetic interface (RMM), without simplifying the magnetic field boundaries. Based on the EJ power law, Kim model, and TA model, the current density distribution of the stator coils is calculated by performing calculations on each turn of each stator coil. Integrate to obtain the instantaneous AC loss of the stator coil, and average it over time to obtain the total AC loss of the stator.
[0033] Step 8: Calculate the AC losses of the rotor coils using rotating domain exchange technology, thereby solving the problems of difficult simulation convergence and long simulation time caused by rotor rotation. This invention develops a technology called rotating domain exchange, which adjusts the traditional simulation model of "rotor rotating, stator fixed" to "rotor fixed, stator rotating in the opposite direction," avoiding the rotational simulation of complex coil structures. Furthermore, the air gap magnetic flux density of the generator remains consistent before and after rotating domain exchange, making the model electromagnetically equivalent to the actual situation. A direct coupling method is used to construct the electromagnetic model of the rotor coils through the CB interface, substituting the material parameters and boundary conditions from the previous steps. Based on the EJ power law, Kim model, and TA model, the current density distribution of the rotor coils is calculated. Integrating the instantaneous AC loss yields the total AC loss of the rotor, which can then be obtained by averaging over time.
[0034] Example: Step 1: Establish a two-dimensional axisymmetric model of the HTS coil. To improve computational efficiency, the three-dimensional HTS coil is simplified into a two-dimensional axisymmetric coil model. During modeling, only the superconducting layer with a width of 4 mm and a thickness of 1 mm is considered; other material layers are ignored, and only the superconducting coil body is modeled, ignoring the air domain to simplify calculations. The established axisymmetric model of the HTS coil is as follows: Figure 1 As shown.
[0035] Step 2: Description of the electromagnetic properties of the superconductor. Electric field strength of the HTS coil. The EJ power-law relationship shown in equation (1) determines that, For the critical electric field, This is the loss index. For depends on magnetic flux density The critical current density can be calculated using the Kim model shown in equation (2). , and These are parameters belonging to the Kim model, used to describe the anisotropy of high-temperature superconducting tapes. They represent the magnetic field components parallel to the tape surface. and magnetic field components perpendicular to the strip surface It can be determined by the Biot-Savart law.
[0036] Step 3: Establish the current density dynamic equation based on the J-model. In the J-model, the current density... The current density is directly used as the state variable to be determined. A dynamic equation for the current density is established through integration, and the expression for the desired quantity is derived. For the two-dimensional axisymmetric coil model, the high-temperature superconductor region... Total magnetic vector potential It can be expressed as equation (3), which shows that It has two components. Among them, It is caused by the applied magnetic field. The generated vector potential With the current used to drive transmission Applying an electric field The generated vector potential The sum of these is an externality. The magnetic vector potential is generated by the interaction between currents and belongs to the internal interaction. Then, by applying Maxwell's equations, EJ's power law, and the Kim model, the current density dynamic equation of the coil model can be established, as shown in equation (4). The vacuum permeability; It is a two-dimensional integral kernel generated using the geometric relationships of the model and the established cylindrical coordinate system; Calculated according to the law of electromagnetic induction, and It is the quantity to be solved, representing the first... The magnitude of the electric field strength of each coil.
[0037] Step 4: Calculate the voltage and critical current. Based on the current constraint condition shown in equation (5), the following can be obtained: The system of linear equations is shown in equation (6). and It can be calculated using equations (7) and (8). Based on the above equations, the electric field of the high-temperature superconducting coil under any transmission current can be calculated. Furthermore, the average voltage of the coil under any transmission current is obtained, and the critical current of the coil is determined by combining the critical current criterion of 1 μV / cm.
[0038] Step 5: After calculating the critical current of the HTS coil, further evaluate its AC losses. First, based on the structural parameters of the HTS motor, a 2D electromagnetic simulation model is constructed using finite element simulation software. The model includes the stator, rotor, air gap, and aluminum barrel shielding structure, with the specific settings as follows: Motor structural parameters: The motor selected in this invention is an 8-pole, 12-slot synchronous generator. The stator adopts a 12-slot structure, and the rotor adopts an 8-pole built-in structure with an air gap width of 5mm. Both the stator and rotor coils are racetrack-shaped coils wound with YBCO superconducting tape. The stator armature winding consists of 12 double-racetrack coils, each with 12 turns. The rotor excitation winding consists of 8 racetrack coil assemblies, each assembly containing 5 racetrack coils, each coil with 60 turns.
[0039] Material parameters: The stator and rotor cores are made of silicon steel sheet DW360_50, the width of YBCO strip is 4mm, the thickness of HTS layer is 1μm, and the critical current under 20K self-field is 1188A.
[0040] Simplification: Losses in the silver, copper, and Hastelloy layers of the YBCO strip are ignored; only the AC loss of the HTS layer is calculated. The thickness of the HTS strip is ignored, and the 3D coil structure is simplified to a 2D model. Since AC losses mainly occur in the straight sections of the coil, the curved sections of the racetrack coil are ignored. The total number of turns in the stator coil is 2×12, and the total number of turns in the rotor coil is 5×60. The structures of the stator and rotor coils are as follows... Figure 2 As shown.
[0041] Step Six: Construct a numerical model based on the TA model to provide a theoretical framework for subsequent loss calculations. Define the current density vector potential in the superconducting domain. Used to solve for the current density of HTS coated conductors. The distribution is shown in equation (9). In the two-dimensional model, its boundary conditions are shown in equation (10). Wherein, It is the vector potential of the current density on the width side of the strip. Let the vector potential of the current density on the other side be denoted as . , Let be the current flowing through a single HTS tape. Define the magnetic field vector potential in both superconducting and non-superconducting domains. Its expression is shown in equation (11), where Permeability, Let be the electrical conductivity, and let the boundary conditions be the magnetic field vector potential. .
[0042] Step 7: Calculate the AC losses of the stator coils using the direct coupling method to avoid boundary simplification errors. The direct coupling method involves directly selecting the coil domain from the HTS generator model to establish the coil model. In COMSOL simulation software, the coupled model is constructed using coefficient-form boundary partial differential equations (CB) and rotating machinery magnetic interface (RMM), without simplifying the magnetic field boundaries. Based on the EJ power law, Kim model, and TA model, the current density distribution of the stator coils at 10 ms can be obtained as follows: Figure 3 As shown, this is then achieved by performing a process on each turn of each stator coil. Points can be earned. Figure 4 The instantaneous AC loss of the stator coil shown can be averaged over time to obtain the total AC loss.
[0043] Step 8: Calculate the rotor coil AC losses using rotating domain exchange technology, thereby solving the problems of difficult simulation convergence and long simulation time caused by rotor rotation. This invention develops a technology called rotating domain exchange, which adjusts the traditional simulation model of "rotor rotating, stator fixed" to "rotor fixed, stator rotating in the opposite direction," avoiding the rotation simulation of complex coil structures. Furthermore, the air gap magnetic flux density of the generator remains consistent before and after rotating domain exchange. This model is electromagnetically equivalent to the actual situation. A schematic diagram of the rotating domain for calculating stator AC losses and rotor AC losses is shown below. Figure 5 As shown. Using a direct coupling method, an electromagnetic model of the rotor coil is constructed via the CB interface, incorporating the material parameters and boundary conditions from the previous steps. Based on the EJ power law, Kim model, and TA model, the current density distribution of the rotor coil at 20 ms can be obtained as follows: Figure 6 As shown, this is then achieved by performing a process on each turn of each rotor coil. Points can be earned. Figure 7 The instantaneous AC loss of the rotor coil shown can be averaged over time to obtain the total AC loss of the rotor coil.
[0044] This invention introduces an integral method based on the J-model, which can quickly calculate the critical current of HTS coils, improving efficiency by more than four times compared to the finite element method. Subsequently, the AC losses of the stator and rotor windings were calculated. For the stator, the total AC loss calculated using a direct coupling model was 15.645 kW, which was compared with the result calculated using an indirect coupling model with simplified boundary conditions. The results show that the indirect coupling model may introduce significant uncertainty in loss estimation, and although the direct coupling model is more complex and time-consuming, it is unavoidable in accurate AC loss estimation. For the rotor, a technique called rotating domain exchange was developed to construct a direct coupling model. The calculated AC loss was 6.268 kW, approximately half the stator loss value. This result differs from the assumption in many previous studies that rotor losses are negligible, confirming that in HTS generators with narrow air gaps and a large number of rotor winding turns, rotor AC losses are not insignificant and should be carefully estimated or optimized.
Claims
1. A method for accurately calculating the critical current and AC loss of a high-temperature superconducting generator coil, characterized in that, Includes the following steps: Step 1: Establish a two-dimensional axisymmetric model of the HTS coil; Step 2: Describe the electromagnetic properties of the superconductor; Step 3: Establish the current density dynamic equation based on the J model; Step 4: Calculate the voltage and critical current; Step 5: After calculating the critical current of the HTS coil, further evaluate its AC losses; Step 6: Construct a numerical model based on the TA model to provide a theoretical framework for subsequent loss calculations; Step 7: Calculate the AC loss of the stator coil using the direct coupling method; Step 8: Calculate the AC loss of the rotor coil using the rotating domain exchange technique.
2. The method for accurately calculating the critical current and AC loss of a high-temperature superconducting generator coil according to claim 1, characterized in that, Step 1 specifically involves: The three-dimensional HTS coil is simplified into a two-dimensional axisymmetric coil model. In the modeling process, only the superconducting layer is considered, other material layers are ignored, and only the superconducting coil body is modeled, ignoring the air domain to simplify the calculation.
3. The method for accurately calculating the critical current and AC loss of a high-temperature superconducting generator coil according to claim 2, characterized in that, Step 2 specifically involves: HTS coil electric field strength The EJ power-law relationship shown in equation (1) determines that, For the critical electric field, The loss index; For depends on magnetic flux density The critical current density is calculated using the Kim model shown in equation (2), where, , and These are parameters belonging to the Kim model, used to describe the anisotropy of high-temperature superconducting tapes; magnetic field components parallel to the tape surface. and magnetic field components perpendicular to the strip surface Determined by the Biot-Savart law; (1) (2)。 4. The method for accurately calculating the critical current and AC loss of a high-temperature superconducting generator coil according to claim 3, characterized in that, Step 3 specifically involves: In the J model, current density The current density is directly used as the state variable to be determined. A dynamic equation for the current density is established through integration, and the expression for the desired quantity is derived. For the two-dimensional axisymmetric coil model, the high-temperature superconductor region... Total magnetic vector potential Represented by equation (3), this formula shows It has two components, where, It is caused by the applied magnetic field. The generated vector potential With the current used to drive transmission Applying an electric field The generated vector potential The sum of these is an externality; The magnetic vector potential is generated by the interaction between currents and belongs to the internal interaction; then, by using Maxwell's equations, EJ power law and Kim model, the current density dynamic equation of the coil model is established, as shown in equation (4), where The vacuum permeability; It is a two-dimensional integral kernel generated using the geometric relationships of the model and the established cylindrical coordinate system; Calculated according to the law of electromagnetic induction It is the quantity to be solved, representing the first... The magnitude of the electric field strength of each coil; Represents the area differential element in two-dimensional space. This represents the integration variable, and other points in space. This indicates the location of the field point to be solved. It is the core state variable of the J model, representing the time-varying current density distribution in the superconducting coil; The time-varying component of the applied magnetic field in the x-direction. The component of the applied magnetic field in the y-direction that varies with time; (3) (4)。 5. The method for accurately calculating the critical current and AC loss of a high-temperature superconducting generator coil according to claim 4, characterized in that, Step 4 specifically involves: Based on the current constraint condition shown in equation (5), we obtain the following about The system of linear equations is shown in equation (6); where and Calculated from equations (7) and (8), It is the element in the i-th row and j-th column of a matrix, used to describe the coupling relationship between the turns of the superconducting coil. Let represent the equivalent driving source in the j-th turn of the coil, i.e., the total excitation source driving the electric field of the j-th turn of the coil; the electric field of the high-temperature superconducting coil under arbitrary transmission current is calculated according to equation (6). Furthermore, the average voltage of the coil under any transmission current is obtained, and the critical current of the coil is determined by combining the critical current criterion of 1 μV / cm. (5) (6) (7) (8) in, This represents the equivalent electric field in superconducting materials.
6. The method for accurately calculating the critical current and AC loss of a high-temperature superconducting generator coil according to claim 5, characterized in that, Step 5 specifically involves: First, based on the structural parameters of the HTS motor, a 2D electromagnetic simulation model was constructed using finite element simulation software, including the stator, rotor, air gap, and aluminum barrel shielding structure. The specific settings are as follows: Motor structural parameters: The motor selected in this invention is an 8-pole 12-slot synchronous generator. The stator adopts a 12-slot structure, and the rotor adopts an 8-pole built-in type with an air gap width of 5mm. Both the stator and rotor coils are racetrack-shaped coils wound with YBCO superconducting strip. The stator armature winding consists of 12 double racetrack coils, each single racetrack coil has 12 turns. The rotor excitation winding consists of 8 racetrack coil assemblies, each assembly contains 5 racetrack coils, and each coil has 60 turns. Material parameters: The stator and rotor cores are made of silicon steel sheet DW360_50, the width of YBCO strip is 4mm, the thickness of HTS layer is 1μm, and the critical current under 20K self-field is 1188A. The losses of the silver, copper, and Hastelloy layers in the YBCO strip are ignored, and only the AC losses of the HTS layer are calculated. The thickness of the HTS strip is ignored, and the 3D coil structure is simplified to a 2D model. Since the AC losses are mainly generated in the straight part of the coil, the curved part of the raceway coil is ignored. The total number of turns of the stator coil is 2×12, and the total number of turns of the rotor coil is 5×60.
7. The method for accurately calculating the critical current and AC loss of a high-temperature superconducting generator coil according to claim 6, characterized in that, Step 6 specifically involves: Define the current density vector potential in the superconducting domain Used to solve for the current density of HTS coated conductors. The distribution is shown in equation (9); in the two-dimensional model, its boundary conditions are shown in equation (10), where, It is the vector potential of the current density on the width side of the strip; Let the vector potential of the current density on the other side be denoted as . ; The current flowing through a single HTS tape; the magnetic field vector potential is defined in both the superconducting and non-superconducting domains. Its expression is shown in equation (11), where Permeability, Let be the electrical conductivity, and let the boundary conditions be the magnetic field vector potential. ; For vector differentiation, denote the curl operation; (9) (10) (11)。 8. The method for accurately calculating the critical current and AC loss of a high-temperature superconducting generator coil according to claim 7, characterized in that, Step 7 specifically involves: The direct coupling method involves directly selecting the coil domain from the HTS generator model to establish the coil model. In the COMSOL simulation software, the coupling model is constructed using the coefficient-form boundary partial differential equation CB and the rotating machinery magnetic interface RMM. Based on the EJ power law, Kim model, and TA model, the current density distribution of the stator coils is calculated by performing calculations on each turn of each stator coil. Integrate to obtain the instantaneous AC loss of the stator coil, and average it over time to obtain the total AC loss of the stator.
9. The method for accurately calculating the critical current and AC loss of a high-temperature superconducting generator coil according to claim 8, characterized in that, Step 8 specifically involves: Using a direct coupling method, the electromagnetic model of the rotor coil is constructed through the CB interface of the coefficient-form boundary partial differential equations. Material parameters and boundary conditions in formulas (10) and (11) are substituted. Based on the EJ power law, Kim model, and TA model, the current density distribution of the rotor coil is calculated. Integrating the instantaneous AC loss yields the total AC loss of the rotor, which is then averaged over time.
10. The method for accurately calculating the critical current and AC loss of a high-temperature superconducting generator coil according to claim 9, characterized in that, The superconducting layer has a width of 4 mm and a thickness of 1 mm.