A three-dimensional finite element modeling method and system for electromagnetic calculation of racetrack-shaped superconducting coils

Abstract

The present invention belongs to the technical field of three-dimensional modeling of superconducting electrical engineering, and more specifically, it relates to a three-dimensional finite element modeling method and system for electromagnetic calculation of racetrack-shaped superconducting coils. The racetrack-shaped superconducting coil is wound by a second-generation high-temperature superconducting conductor, and geometrically comprises a plurality of arc parts and a plurality of straight line parts. The method solves the arc parts and the straight line parts respectively based on the cylindrical coordinate system and the rectangular coordinate system of the T-A formula, and then sets the corresponding current boundary conditions according to the direction and value of the transmission current in the coil, ensures the continuity of the current boundary conditions of adjacent parts, and then calculates the numerical solution of the electromagnetic field of the coil. The present invention solves the disadvantage that the two-dimensional finite element model of the superconducting coil cannot solve the electromagnetic characteristics such as the AC loss of the arc part of the superconducting coil, resulting in the inability to obtain accurate AC loss calculation results.

Description

Technical Field

[0001] The present invention belongs to the technical field of three-dimensional modeling of superconducting electrical engineering, and more specifically, relates to a three-dimensional finite element modeling method and system for electromagnetic calculation of racetrack-shaped superconducting coils. Background Art

[0002] Offshore high-power wind power generation systems are an important technology to alleviate energy shortages, and superconducting motors with outstanding advantages such as high torque density and high efficiency have broad application scenarios in the field of offshore wind power generation. In the design process of superconducting equipment such as superconducting motors, it is necessary to accurately calculate the AC loss of superconducting coils to determine the cooling power and cost of the cryogenic cooling system, and evaluate the feasibility of the superconducting coil design scheme through the calculated AC loss. Establishing a finite element model of a superconducting coil is an essential step in analyzing the characteristics of the superconducting coil such as AC loss under complex magnetic fields.

[0003] At present, superconducting coils wound by second-generation high-temperature superconducting coated conductors are mainly modeled by the TA formula. In addition, the nonlinear resistance characteristics of second-generation high-temperature superconducting coated conductors can be described by the Kim critical state model and the EJ power law. By coupling the TA formula with the Kim critical state model and the EJ power law, a two-dimensional finite element model of the superconducting coil can be established and used to analyze the AC loss characteristics and critical current characteristics of the superconducting coil.

[0004] Chinese invention patent CN114999595A discloses a finite element-based method and system for simulating and modeling the quenching of a superconducting coil as a whole, including constructing a geometric model of the superconducting coil and adding physical property functions to each layer; establishing a geometric model of a cooling medium and adding physical property functions; using the superconducting coil model as a heat source, setting the interface between the superconducting coil and the cooling medium as a heat flux boundary, and modeling the electromagnetic field of the superconducting coil through the H equation; using the temperature calculated under the current Joule heat generated by the heat source to calculate the current density of the electromagnetic field; obtaining the magnetic field strength under the new current density; obtaining the current density under the new magnetic field strength, and using it to calculate and update the Joule heat generated by the heat source; adding boundary conditions of the electromagnetic field through point-by-point constraints, solving the multi-physical field coupling quenching calculation model of the superconducting coil to be simulated, and obtaining the distribution of each physical field.

[0005] In summary, the two-dimensional finite element model of the superconducting coil cannot solve the electromagnetic characteristics such as the AC loss of the arc part of the racetrack-shaped superconducting coil, resulting in the inability to obtain accurate AC loss calculation results. Therefore, it is necessary to study a finite element model that can solve the arc part of the racetrack-shaped superconducting coil. A modeling method that can make up for the shortcoming that the two-dimensional finite element model of the racetrack-shaped superconducting coil cannot solve the arc part of the racetrack-shaped superconducting coil is urgently needed to model the superconducting coil more accurately. Summary of the invention

[0006] The present invention aims to overcome at least one defect of the above-mentioned prior art and provide a three-dimensional finite element modeling method for electromagnetic calculation of a racetrack-shaped superconducting coil, so as to solve the problem that the two-dimensional finite element model of the superconducting coil cannot solve the electromagnetic characteristics such as the AC loss of the arc part of the superconducting coil, resulting in the inability to obtain accurate AC loss calculation results.

[0007] The detailed technical scheme of the present invention is as follows:

[0008] A three-dimensional finite element modeling method for electromagnetic calculation of a racetrack-shaped superconducting coil, the method comprising:

[0009] S1: Establish a three-dimensional geometric model of a racetrack-shaped superconducting coil or a superconducting device including a superconducting coil;

[0010] S2: Establish a global rectangular coordinate system with the geometric center point of the racetrack-shaped superconducting coil as the coordinate origin R 0, the clockwise direction along the superconducting coil is defined as the current transmission direction;

[0011] Will be in the coordinate system R The multiple straight lines in the positive and negative directions of the x-axis and the positive and negative directions of the y-axis are named Pi~Pn areas respectively; R The multiple arc parts in the positive and negative directions of the x-axis and the positive and negative directions of the y-axis are named Uv~Uz areas in sequence;

[0012] S3: For each arc part, take its own center as the coordinate origin, select the same positive z-axis direction as the coordinate system R0, and establish its own cylindrical coordinate system C v ~C z ;

[0013] S4, cylindrical coordinate system C v ~C z The coordinate origin of is taken as the origin, and the positive directions of the x-axis, y-axis, and z-axis that are the same as those of the coordinate system R0 are selected to establish rectangular coordinate systems respectively. R v ~R z ;

[0014] S5: For the arc part Uv~Uz, first, based on the respective cylindrical coordinate systems established in S4 C v ~C z , according to the cylindrical coordinate solution system of the TA formula, write the electromagnetic calculation equations;

[0015] Then, the cylindrical coordinate system is transformed intoC v ~C z The electromagnetic calculation equations under are converted to the rectangular coordinate system R v ~R z The following form;

[0016] Finally, the rectangular coordinate system is transformed by coordinate transformation method. R v ~R z The electromagnetic calculation equations under are converted to the global rectangular coordinate system R 0 below the form;

[0017] S6: For the straight line part Pi~Pn, based on the global rectangular coordinate system R 0 and coordinate transformation, according to the rectangular coordinate system of TA formula, write the electromagnetic calculation equations;

[0018] S7: For the three-dimensional geometric model established in S1, set material physical properties for all geometric entities and air domains;

[0019] Furthermore, the physical properties of the material include electrical conductivity, magnetic permeability and relative dielectric constant.

[0020] S8: For the superconducting coil modeling part in the three-dimensional geometric model established in S1, in the partial differential equation module, first, input the electromagnetic calculation equations of each part of the superconducting coil finally obtained from S2 to S6, including: the calculation part of the electric field intensity E with the current vector potential T as the independent variable in the TA formula solution system, the critical current density based on the Kim critical state model J c Calculation part: Nonlinear resistivity based on EJ power law r HTS Calculation part; then, setting corresponding current boundary conditions at the boundaries of each part of the superconducting coil to complete the T field numerical modeling of the superconducting coil part in the three-dimensional finite element model;

[0021] S9: For the superconducting coil modeling part in the three-dimensional geometric model established in S1, in the electromagnetic field module, the numerical expression of the magnetic field intensity H with the magnetic field vector potential A as the independent variable in the TA formula solution system is realized through the Maxwell equations, and the A field numerical modeling of the superconducting coil part in the three-dimensional finite element model is completed. Combined with S11, the electromagnetic field numerical modeling of the superconducting coil part in the three-dimensional finite element model is finally realized;

[0022] S10: For the non-superconducting coil modeling part in the three-dimensional geometric model established in S1, in the electromagnetic field module, the electric field intensity E and the magnetic field intensity H of the non-superconducting coil part are numerically expressed through the Maxwell equations, thereby completing the electromagnetic field numerical modeling of the non-superconducting coil part in the three-dimensional finite element model;

[0023] S11: Meshing all geometric entities and air domains for the three-dimensional geometric model established in S1;

[0024] S12: For the three-dimensional geometric model established in S1, adjust the solver's total solution time, calculation step, result output step, calculation tolerance and other parameters. The model can be used for the analysis and solution of electromagnetic calculations of superconducting coils and their superconducting devices.

[0025] Furthermore, the S6 specifically includes:

[0026] S61: Based on coordinate system R 0 is the origin of the coordinate system. R The negative direction of the x-axis, the negative direction of the y-axis, and the negative direction of the z-axis of 0 are the new positive directions of the x-axis, y-axis, and z-axis, and the coordinate system is established. R 0Completely opposite rectangular coordinate system R t ;

[0027] S62: For the straight line portion in the positive direction of the x-axis, based on the global rectangular coordinate system R 0. According to the rectangular coordinate solution system of the TA formula, write the electromagnetic calculation equations;

[0028] S63: For the straight line portion in the negative direction of the x-axis, first, based on the rectangular coordinate system R t , according to the rectangular coordinate system of the TA formula, write the electromagnetic calculation equations; secondly, through the transformation of the positive and negative coordinate systems, the rectangular coordinate system R t The electromagnetic calculation equations are converted to the global rectangular coordinate system R 0 below the form;

[0029] S64: For y The linear part of the positive axis is firstly calculated in the global rectangular coordinate system. R 0 as the origin, and select the coordinate system R 0Same z The positive direction of the axis is the opposite direction of the current transmission direction of the straight part. y The positive direction of the axis is selected according to the right-hand principle, perpendicular to the current transmission direction of the straight part. x Axis positive direction, establish rectangular coordinate system R f, based on the rectangular coordinate system R f , according to the rectangular coordinate system of the TA formula, write the electromagnetic calculation equations; secondly, through the transformation of the positive and negative coordinate systems, transform the above rectangular coordinate system R f The electromagnetic calculation equations are converted to the global rectangular coordinate system R 0 below the form;

[0030] S65: For y The linear part in the negative direction of the axis is firstly calculated in the global rectangular coordinate system. R t The origin of the coordinate system is R t Same z The positive direction of the axis is the opposite direction of the current transmission direction of the straight part. y The positive direction of the axis is selected according to the left-hand principle, perpendicular to the current transmission direction of the straight part x Axis positive direction, establish rectangular coordinate system R b , based on the rectangular coordinate system R b , according to the rectangular coordinate system of the TA formula, write the electromagnetic calculation equations; secondly, through coordinate transformation, transform the above rectangular coordinate system R b The electromagnetic calculation equations are converted to the global rectangular coordinate system R t Finally, through the transformation of the positive and negative coordinate systems, the above rectangular coordinate system R t The electromagnetic calculation equations are converted to the global rectangular coordinate system R 0 form.

[0031] The superconducting coil is wound with a second generation high temperature superconducting coated conductor, usually a rare earth barium copper oxide coated conductor.

[0032] The superconducting coil includes a single pancake coil or a multi-pancake coil group. The single pancake coil is a superconducting coil having only one superconducting coil stacked in the z-axis direction of the superconducting coil, and the multi-pancake superconducting coil group is a superconducting coil having multiple superconducting coils stacked in the z-axis direction of the superconducting coil.

[0033] The superconducting coil modeling part in the three-dimensional finite element model can be combined with a homogenization method to establish a homogenized equivalent model of the superconducting coil, or can be combined with no homogenization method to establish a complete and accurate model of the superconducting coil.

[0034] In another aspect of the present invention, a system for implementing a three-dimensional finite element modeling method for electromagnetic calculation of a racetrack-shaped superconducting coil is provided, the system comprising:

[0035] at least one processor; and

[0036] A memory storing instructions, when the instructions are executed by the at least one processor, enables the at least one processor to execute the three-dimensional finite element modeling method for electromagnetic calculation of a racetrack-shaped superconducting coil as described above.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] The present invention provides a three-dimensional finite element modeling method and system for electromagnetic calculation of a racetrack-shaped superconducting coil, which divides the racetrack-shaped superconducting coil into an arc part and a straight part, and establishes an independent rectangular coordinate system for each straight part, and an independent cylindrical coordinate system for each arc part, and then writes the rectangular coordinate system and cylindrical coordinate system of the TA formula for each straight part and each arc part respectively for solving, and then sets the corresponding current boundary conditions according to the direction and value of the transmission current in the coil, and then calculates the numerical solution of the electromagnetic field of the coil through a transient solver. The three-dimensional finite element model established by the modeling method can additionally solve the arc part of the racetrack-shaped superconducting coil and the arc part of other special structure superconducting coils, so that the established three-dimensional finite element model is closer to the actual situation of the superconducting coil, and the electromagnetic characteristics such as critical current and AC loss of the straight part and the arc part of the racetrack-shaped superconducting coil can be obtained through the model, thereby providing a more comprehensive reference basis for the design of superconducting equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A flow chart of the three-dimensional finite element modeling method for electromagnetic calculation of the racetrack-shaped superconducting coil of the present invention;

[0040] Figure 2 It is a schematic diagram of the structure of the racetrack-shaped superconducting coil and other special structure superconducting coils of the present invention;

[0041] Figure 3 A multi-coordinate system configuration of a racetrack-shaped superconducting coil according to an embodiment of the present invention;

[0042] Figure 4 The multi-coordinate system configuration of the superconducting coil 1 of the special structure of the present invention;

[0043] Figure 5 The multi-coordinate system configuration of the superconducting coil 2 of the special structure of the example of the present invention;

[0044] Figure 6 A schematic diagram of a solution process of a set of electromagnetic calculation equations for a typical structure of a racetrack-shaped superconducting coil according to an embodiment of the present invention;

[0045] Figure 7 A schematic diagram of a solution process of a group of electromagnetic calculation equations for a special structure superconducting coil 1 of an example of the present invention;

[0046] Figure 8 It is a schematic diagram of the solution process of the electromagnetic calculation equations of the special structure superconducting coil 2 of the example of the present invention;

[0047] Fig. 9 Schematic diagram of applying boundary conditions to the finite element model of a racetrack-shaped superconducting coil according to an example of the present invention. DETAILED DESCRIPTION

[0048] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0049] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0050] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. In addition, it should also be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0051] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0052] Example 1

[0053] Ginseng Figure 1 This embodiment provides a three-dimensional finite element modeling method for electromagnetic calculation of a racetrack-shaped superconducting coil, the method comprising:

[0054] S1: In finite element analysis software, a three-dimensional geometric model of a racetrack-shaped superconducting coil or a superconducting device including the superconducting coil is established.

[0055] Preferably, the superconducting coil is wound by a second generation high temperature superconducting coated conductor, usually a rare earth barium copper oxide coated conductor.

[0056] Preferably, the superconducting coil includes a single pancake coil or a multi-pancake coil group, the single pancake coil is a superconducting coil with only one superconducting coil stacked in the z-axis direction, and the multi-pancake superconducting coil group is a superconducting coil with multiple superconducting coils stacked in the z-axis direction.

[0057] The superconducting coil modeling part in the three-dimensional finite element model can be combined with a homogenization method to establish a homogenized equivalent model of the superconducting coil, or can be combined with no homogenization method to establish a complete and accurate model of the superconducting coil.

[0058] S2: Establish a global rectangular coordinate system with the geometric center point of the racetrack-shaped superconducting coil as the coordinate origin R 0, the clockwise direction along the superconducting coil is defined as the current transmission direction;

[0059] Will be in the coordinate system R The multiple straight lines in the positive and negative directions of the x-axis and the positive and negative directions of the y-axis are named Pi~Pn areas respectively; R The multiple arc portions on the positive and negative directions of the x-axis and the positive and negative directions of the y-axis are named Uv~Uz areas respectively.

[0060] Specifically, the racetrack-shaped superconducting coil is as follows Figure 2 As shown, including: Figure 2 (a) Typical structure of racetrack-shaped superconducting coil. Figure 2 (b) Special structure superconducting coil 1 and Figure 2 (c) Special structure superconducting coil 2. Take the geometric center points of the three superconducting coils as the coordinate origin and establish the following Figure 3 , Figure 4 , Figure 5 The spatial rectangular coordinate system shown in R 0, R 0Including the global rectangular coordinate system of the typical structure of the racetrack-shaped superconducting coil R 10 , Special structure superconducting coil 1 Global rectangular coordinate system R 20 and the global rectangular coordinate system of the special structure superconducting coil 2 R 30 .

[0061] like Figure 3 As shown, the typical structure of the racetrack-shaped superconducting coil is located in the coordinate system R 10 The straight line parts on the positive and negative directions of the x-axis are named P11 and P12 respectively. R 10 The arc parts in the positive direction of the y-axis and the negative direction of the y-axis are named U11 area and U12 area respectively;

[0062] like Figure 4 As shown, the special structure superconducting coil 1 is located in the coordinate system R 20 of x Axis positive direction and x The straight line parts on the negative direction of the axis are named P21 area and P22 area respectively. R 20 of y The straight line part in the positive direction of the axis is named P23 area.R 20 of y The arc parts on the positive direction of the axis are named U21 area and U22 area respectively. R 20 of y The arc part in the negative direction of the axis is named as the U23 area;

[0063] like Figure 5 As shown, the special structure superconducting coil 2 is located in the coordinate system R 30 of x The straight line part in the positive direction of the axis is named P31 area, which is located in the coordinate system R 30 The straight lines on the negative x-axis are named P32 and P33 respectively. R 30 of y Axis positive direction y The arc parts on the negative direction of the axis are named U31 area and U32 area respectively. R The arc parts on the negative direction of the x-axis of 0 are named U33 area, U34 area, and U35 area.

[0064] S3: Establish the cylindrical coordinate system of the arc part, such as Figure 3 As shown in the figure, for the two arc parts (U11 and U12) of the typical structure of the racetrack-shaped superconducting coil, their respective centers are taken as the coordinate origins, and the coordinate system is selected. R 10 Same z Axis positive direction, respectively establish cylindrical coordinate system C 11 and C 12 ;

[0065] S4: Establish a rectangular coordinate system with the origin of the cylindrical coordinate system as the origin, such as Figure 3 As shown in the figure, the typical structure of the racetrack superconducting coil is represented by the cylindrical coordinate system C 11 and C 12 The coordinate origin is the origin, and the coordinate system R 10 Same x axis, y axis, z Axis positive direction, respectively establish rectangular coordinate system R 11 and R 12 ;

[0066] S5: Figure 6FIG. 1 is a schematic diagram of a flow chart of solving the electromagnetic calculation equations of the typical structure of the racetrack-shaped superconducting coil according to an embodiment of the present invention. For the two arc parts (U11 and U12) of the typical structure of the racetrack-shaped superconducting coil, first, based on the cylindrical coordinate systems corresponding to them established in S4, C 11 and C 12 , solve the series of electromagnetic calculation equations according to the cylindrical coordinate system of the TA formula;

[0067] Then, the above coordinate transformation method is used to transform C 11 and C 12 The electromagnetic calculation equations in the cylindrical coordinate system are converted to the rectangular coordinate system R 11 and R 12 The following form;

[0068] Finally, the above coordinate transformation method is used to transform R 11 and R 12 The electromagnetic calculation equations in the rectangular coordinate system are converted to the global rectangular coordinate system R 10 The following form.

[0069] S6: For the straight line part Pi~Pn, based on the global rectangular coordinate system R 0 and coordinate transformation, according to the rectangular coordinate system of TA formula, write the electromagnetic calculation equations;

[0070] Preferably, the specific processing steps of the typical structure of the racetrack-shaped superconducting coil described in this embodiment are as follows:

[0071] S61: Figure 3 As shown, the coordinate system of the typical structure of the racetrack superconducting coil R 10 The coordinate origin of the coordinate system is R 10 of x Negative axis direction, y Negative axis direction, z The negative direction of the axis is the new x axis, y axis, z Axis positive direction, establish and coordinate system R 10 Completely opposite rectangular coordinate system R 13 ;

[0072] S62: Figure 6As shown, for the straight line portion in the positive direction of the x-axis, that is, the straight line portion P11 of the typical structure of the racetrack-shaped superconducting coil, it is directly based on the global rectangular coordinate system R 10 , solve the series of electromagnetic calculation equations according to the rectangular coordinate system of the TA formula;

[0073] S63: Figure 6 As shown, for the straight line portion in the negative direction of the x-axis, that is, the straight line portion P12 of the typical structure of the racetrack-shaped superconducting coil, first, based on the rectangular coordinate system R 13 , solve the series of electromagnetic calculation equations according to the rectangular coordinate system of the TA formula; secondly, use the coordinate transformation method to transform the above rectangular coordinate system R 13 The electromagnetic calculation equations are converted to the global rectangular coordinate system R 10 The following form;

[0074] There is no straight line part in the y-axis direction of the typical structure of the racetrack-shaped superconducting coil, which can be omitted.

[0075] S7: For the three-dimensional geometric model established in S1, set material physical properties for all geometric entities and air domains;

[0076] Furthermore, the physical properties of the material include electrical conductivity, magnetic permeability and relative dielectric constant.

[0077] S8: For the superconducting coil modeling part in the three-dimensional geometric model established in S1, in the partial differential equation module, first, input the electromagnetic calculation equations of each part of the superconducting coil finally obtained from S2 to S63, including: the calculation part of the electric field intensity E with the current vector potential T as the independent variable in the TA formula solution system, the critical current density based on the Kim critical state model J c Calculation part: Nonlinear resistivity based on EJ power law r HTS Calculation part; then, set the corresponding current boundary conditions at the boundaries of each part of the superconducting coil, such as Fig. 9 As shown, a boundary condition of T=0 is set on the upper surface of the superconducting coil, and a boundary condition of T=1 is set on the lower surface of the superconducting coil. f / d boundary conditions, where I f The superconducting coil transmits current, d is the thickness of the second-generation high-temperature superconducting coating conductor, and finally the current direction boundary conditions are set for the superconducting coil. Fig. 9 The current transmission direction shown on the right completes the T field numerical modeling of the superconducting coil part in the three-dimensional finite element model;

[0078] S9: For the superconducting coil modeling part in the three-dimensional geometric model established in S1, in the electromagnetic field module, the numerical expression of the magnetic field intensity H with the magnetic field vector potential A as the independent variable in the TA formula solution system is realized through the Maxwell equations, and the A field numerical modeling of the superconducting coil part in the three-dimensional finite element model is completed. Combined with S11, the electromagnetic field numerical modeling of the superconducting coil part in the three-dimensional finite element model is finally realized;

[0079] S10: For the non-superconducting coil modeling part in the three-dimensional geometric model established in S1, in the electromagnetic field module, the electric field intensity E and the magnetic field intensity H of the non-superconducting coil part are numerically expressed through the Maxwell equations, thereby completing the electromagnetic field numerical modeling of the non-superconducting coil part in the three-dimensional finite element model;

[0080] S11: Meshing all geometric entities and air domains for the three-dimensional geometric model established in S1;

[0081] S12: For the three-dimensional geometric model established in S1, adjust the solver's total solution time, calculation step, result output step, calculation tolerance and other parameters. The model can be used for the analysis and solution of electromagnetic calculations of superconducting coils and their superconducting devices.

[0082] When establishing a three-dimensional finite element model of a superconducting coil with a special structure or a superconducting device containing the same, the superconducting coil is divided into a number of arc parts and straight line parts according to the structural form of the special structure superconducting coil, and the cylindrical coordinate system and the rectangular coordinate system corresponding to each arc part and the straight line part are respectively established with reference to the methods of S2 to S63, and the above-mentioned cylindrical coordinate system and the rectangular coordinate system are successively transformed into the global rectangular coordinate system through the coordinate transformation method, and then S7 to S12 are implemented to complete the modeling analysis.

[0083] Example 2

[0084] Based on Example 1, the difference from Example 1 is that the racetrack-shaped superconducting coil processed in this example is a special structure superconducting coil 1, and the difference from Example 1 in S3 to S6 is that:

[0085] S3: Figure 4 As shown, for the three arc parts (U21, U22, U23) of the special structure superconducting coil 1, the center of each circle is taken as the coordinate origin, and the coordinate system is selected. R 20 Same z Axis positive direction, respectively establish cylindrical coordinate system C 21 , C 22 , C 23 ;

[0086] S4: Figure 4 As shown, for the special structure superconducting coil 1, the cylindrical coordinate system C 21 , C 22 , C 23 The coordinate origin is the origin, and the coordinate system R 20 Same x axis, y axis, z Axis positive direction, respectively establish rectangular coordinate system R 21 , R 22 , R 23 ,

[0087] S5: Figure 7 As shown, for the three arc parts (U21, U22, U23) of the special structure superconducting coil 1, first, based on the cylindrical coordinate systems corresponding to them established in S4 C 21 , C 22 , C 23 , solve the series of electromagnetic calculation equations according to the cylindrical coordinate system of the TA formula; secondly, use the coordinate transformation method to transform the above C 21 , C 22 , C 23 The electromagnetic calculation equations in the cylindrical coordinate system are converted to the rectangular coordinate system R 21 , R 22 , R 23 Finally, with the help of coordinate transformation method, the above R 21 , R 22 , R 23 The electromagnetic calculation equations in the rectangular coordinate system are converted to the global rectangular coordinate system R 20 The following form;

[0088] S6: For the straight line part Pi~Pn, based on the global rectangular coordinate system R 0 and coordinate transformation, according to the rectangular coordinate system of the TA formula, write the electromagnetic calculation equations; the specific processing steps for the special structure superconducting coil 1 are as follows:

[0089] S61: Figure 4 As shown in the coordinate system R 20 The coordinate origin of the coordinate system is R 20 of x Negative axis direction, y Negative axis direction, z The negative direction of the axis is the new x axis, y axis, z Axis positive direction, establish and coordinate system R 20 Completely opposite rectangular coordinate system R 25 ;

[0090] S62: Figure 7 As shown, for the straight line portion in the positive direction of the x-axis, that is, the straight line portion P21 of the special structure superconducting coil 1, it is directly based on the global rectangular coordinate system R 20 , solve the series of electromagnetic calculation equations according to the rectangular coordinate system of the TA formula;

[0091] S63: Figure 7 As shown, for the straight line portion in the negative direction of the x-axis, that is, the straight line portion P22 of the special structure superconducting coil 1, first, based on the rectangular coordinate system R 25 , according to the rectangular coordinate system of the TA formula, solve the body series to write the electromagnetic calculation equations; secondly, through the transformation of the positive and negative coordinate systems, the rectangular coordinate system R 25 The electromagnetic calculation equations under are converted to the global rectangular coordinate system R 20 The following form;

[0092] S64: For y The straight line portion in the positive direction of the axis is the straight line portion P23 of the special structure superconducting coil 1. First, the global rectangular coordinate system R 0 as the origin, and select the coordinate system R 0Same z The positive direction of the axis is the opposite direction of the current transmission direction of the straight line part P23. y The positive direction of the axis is selected according to the right-hand principle, perpendicular to the current transmission direction of the straight part. x Axis positive direction, establish rectangular coordinate system R 24 , based on the rectangular coordinate system R 24, according to the rectangular coordinate system of the TA formula, write the electromagnetic calculation equations; secondly, through the transformation of the positive and negative coordinate systems, transform the above rectangular coordinate system R 24 The electromagnetic calculation equations are converted to the global rectangular coordinate system R 20 The following form;

[0093] The special structure superconducting coil 1 has no straight line portion in the negative direction of the y-axis and can be omitted.

[0094] Example 3

[0095] Based on Example 1, the difference from Example 1 is that the racetrack-shaped superconducting coil processed in this example is a special structure superconducting coil 2, and the difference from Example 1 in S3 to S6 is that:

[0096] S3: Figure 5 As shown, for the five arc parts (U31, U32, U33, U34, U35) of the special structure superconducting coil 2, the center of each circle is taken as the coordinate origin, and the coordinate system is selected. R 30 Same z Axis positive direction, respectively establish cylindrical coordinate system C 31 , C 32 , C 33 、C 34 , C 34 ;

[0097] S4: Figure 5 As shown, for the special structure superconducting coil 2, the cylindrical coordinate system C 31 , C 32 , C 33 , C 34 , C 35 The coordinate origin is the origin, and the coordinate system R 30 Same x axis, y axis, z Axis positive direction, respectively establish rectangular coordinate system R 31 , R 32 , R 33 , R 34 、R 35 ;

[0098] S5: Figure 8 As shown, for the five arc parts (U31, U32, U33, U34, U35) of the special structure superconducting coil 2, first, based on the cylindrical coordinate systems corresponding to them established in S4, C 31 , C 32 , C 33 , C 34 , C 35 , solve the series of electromagnetic calculation equations according to the cylindrical coordinate system of the TA formula; secondly, use the coordinate transformation method to transform the above C 31 , C 32 , C 33 , C 34 , C 35 The electromagnetic calculation equations in the cylindrical coordinate system are converted to the rectangular coordinate system R 31 , R 32 , R 33 , R 34 , R 35 Finally, with the help of coordinate transformation method, the above R 31 , R 32 , R 33 , R 34 , R 35 The electromagnetic calculation equations in the rectangular coordinate system are converted to the global rectangular coordinate system R 30 The following form;

[0099] S6: For the straight line part Pi~Pn, based on the global rectangular coordinate system R 0 and coordinate transformation, according to the rectangular coordinate system of the TA formula, write the electromagnetic calculation equations; the specific processing steps for the special structure superconducting coil 2 are as follows:

[0100] S61: Figure 5 As shown in the coordinate system R 30 The coordinate origin of the coordinate system is R 30 of xNegative axis direction, y Negative axis direction, z The negative direction of the axis is the new x axis, y axis, z Axis positive direction, establish and coordinate system R 30 Completely opposite rectangular coordinate system R 36 ;

[0101] S62: Figure 8 As shown, for the straight line portion in the positive direction of the x-axis, that is, the straight line portion P31 of the special structure superconducting coil 2, it is directly based on the global rectangular coordinate system R 30 , according to the rectangular coordinates of the TA formula, solve the series of electromagnetic calculation equations;

[0102] S63: Figure 8 As shown, for the straight line portion in the negative direction of the x-axis, that is, the straight line portion P32 and P33 of the special structure superconducting coil 2, first, based on the rectangular coordinate system R 36 , according to the rectangular coordinate system of the TA formula, solve the body series to write the electromagnetic calculation equations; secondly, with the help of the coordinate transformation method, the rectangular coordinate system R 36 The two sets of electromagnetic calculation equations under are converted to the global rectangular coordinate system R 30 The following form;

[0103] There is no straight line part in the y-axis direction of the typical structure of the racetrack-shaped superconducting coil, which can be omitted.

[0104] Example 4

[0105] This embodiment provides a system for implementing a three-dimensional finite element modeling method for electromagnetic calculation of a racetrack-shaped superconducting coil, the system comprising:

[0106] at least one processor; and

[0107] A memory storing instructions, when the instructions are executed by the at least one processor, enables the at least one processor to execute the three-dimensional finite element modeling method for electromagnetic calculation of a racetrack-shaped superconducting coil as described above.

[0108] In this embodiment, the system includes but is not limited to: personal computers, server computers, workstations, desktop computers, laptop computers, notebook computers, mobile computing devices, smart phones, tablet computers, cellular phones, personal digital assistants (PDAs), handheld devices, messaging devices, wearable computing devices, consumer electronic devices, etc.

[0109] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the technical solution of the present invention, and are not intended to limit the specific implementation methods of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the claims of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A three-dimensional finite element modeling method for electromagnetic calculation of racetrack-shaped superconducting coils, characterized in that: The method comprises: S1: Establish a three-dimensional geometric model of a racetrack-shaped superconducting coil or a superconducting device including a superconducting coil; S2: Establish a global rectangular coordinate system with the geometric center point of the racetrack-shaped superconducting coil as the coordinate origin R 0, the clockwise direction along the superconducting coil is defined as the current transmission direction; Will be in the coordinate system R The multiple straight lines in the positive and negative directions of the x-axis and the positive and negative directions of the y-axis are named Pi~Pn areas respectively; R The multiple arc parts in the positive and negative directions of the x-axis and the positive and negative directions of the y-axis are named Uv~Uz areas in sequence; S3: For each arc part, take its own center as the coordinate origin and select R 0 The same positive z-axis direction, respectively establish their own cylindrical coordinate system C v ~C z ; S4, cylindrical coordinate system C v ~C z The coordinate origin is the origin, and the coordinate system R 0 The same x-axis, y-axis, and z-axis positive directions are used to establish rectangular coordinate systems. R v ~ R z ; S5: For the arc part Uv~Uz, first, based on the respective cylindrical coordinate systems established in S4 C v ~C z , according to the cylindrical coordinate solution system of the TA formula, write the electromagnetic calculation equations; Then, the cylindrical coordinate system is transformed into C v ~C z The electromagnetic calculation equations under are converted to the rectangular coordinate system R v ~ R z The following form; Finally, the rectangular coordinate system is transformed by coordinate transformation method. R v ~R z The electromagnetic calculation equations under are converted to the global rectangular coordinate system R 0 below the form; S6: For the straight line part Pi~Pn, based on the global rectangular coordinate system R 0 and coordinate transformation, according to the rectangular coordinate system of TA formula, write the electromagnetic calculation equations; S7: For the three-dimensional geometric model established in S1, set material physical properties for all geometric entities and air domains; S8: For the superconducting coil modeling part in the three-dimensional geometric model established in S1, in the partial differential equation module, the electromagnetic calculation equation group of each part of the superconducting coil finally obtained from S2 to S6 is input; then, the corresponding current boundary conditions are set at the boundaries of each part of the superconducting coil to complete the T field numerical modeling of the superconducting coil part in the three-dimensional finite element model; S9: For the superconducting coil modeling part in the three-dimensional geometric model established in S1, in the electromagnetic field module, the numerical expression of the magnetic field intensity H with the magnetic field vector potential A as the independent variable in the TA formula solution system is realized through the Maxwell equations, and the A field numerical modeling of the superconducting coil part in the three-dimensional finite element model is completed; S10: For the non-superconducting coil modeling part in the three-dimensional geometric model established in S1, in the electromagnetic field module, the electric field intensity E and the magnetic field intensity H of the non-superconducting coil part are numerically expressed through the Maxwell equations, thereby completing the electromagnetic field numerical modeling of the non-superconducting coil part in the three-dimensional finite element model; S11: Meshing all geometric entities and air domains for the three-dimensional geometric model established in S1; S12: For the three-dimensional geometric model established in S1, adjust the total solution time, calculation step, result output step and calculation tolerance parameters of the solver. The model can be used for the analysis and solution of electromagnetic calculations of superconducting coils and their superconducting devices.

2. A three-dimensional finite element modeling method for electromagnetic calculation of racetrack-shaped superconducting coil according to claim 1, characterized in that: The S6 specifically includes: S61: Coordinate system R 0 is the origin of the coordinate system. R The negative direction of the x-axis, the negative direction of the y-axis, and the negative direction of the z-axis of 0 are the new positive directions of the x-axis, y-axis, and z-axis, and the coordinate system is established. R 0Completely opposite rectangular coordinate system R t ; S62: For the straight line portion in the positive direction of the x-axis, based on the global rectangular coordinate system R 0. According to the rectangular coordinate solution system of the TA formula, write the electromagnetic calculation equations; S63: For the straight line portion in the negative direction of the x-axis, first, based on the rectangular coordinate system R t , according to the rectangular coordinate system of the TA formula, write the electromagnetic calculation equations; secondly, through the transformation of the positive and negative coordinate systems, transform the above rectangular coordinate system R t The electromagnetic calculation equations are converted to the global rectangular coordinate system R 0 below the form; S64: For the straight line portion in the positive direction of the y-axis, first, in the global rectangular coordinate system R 0 as the origin, and select the coordinate system R 0 The same z-axis positive direction, the opposite direction of the current transmission direction of the straight part is the y-axis positive direction, according to the right-hand system principle, the x-axis positive direction is selected perpendicular to the current transmission direction of the straight part to establish a rectangular coordinate system R f , based on the rectangular coordinate system R f , according to the rectangular coordinate system of the TA formula, write the electromagnetic calculation equations; secondly, through the transformation of the positive and negative coordinate systems, transform the above rectangular coordinate system R f The electromagnetic calculation equations are converted to the global rectangular coordinate system R 0 below the form; S65: For the straight line portion in the negative direction of the y-axis, first, in the global rectangular coordinate system R t The origin of the coordinate system is R t The same z-axis positive direction, the opposite direction of the current transmission direction of the straight part is the y-axis positive direction, according to the left-handed principle, the x-axis positive direction is selected perpendicular to the current transmission direction of the straight part to establish a rectangular coordinate system R b , based on the rectangular coordinate system R b , according to the rectangular coordinate system of the TA formula, write the electromagnetic calculation equations; secondly, through coordinate transformation, transform the above rectangular coordinate system R b The electromagnetic calculation equations are converted to the global rectangular coordinate system R t Finally, through the transformation of the positive and negative coordinate systems, the above rectangular coordinate system R t The electromagnetic calculation equations are converted to the global rectangular coordinate system R 0 form.

3. A three-dimensional finite element modeling method for electromagnetic calculation of racetrack-shaped superconducting coil according to claim 1, characterized in that: The superconducting coil is wound by a second-generation high-temperature superconducting coated conductor, which is a rare earth barium copper oxide coated conductor.

4. A three-dimensional finite element modeling method for electromagnetic calculation of racetrack-shaped superconducting coil according to claim 1, characterized in that: The superconducting coil includes a single pancake coil or a multi-pancake coil group. The single pancake coil is a superconducting coil with only one superconducting coil stacked in the z-axis direction of the superconducting coil, and the multi-pancake coil group is a superconducting coil with multiple superconducting coils stacked in the z-axis direction of the superconducting coil.

5. A three-dimensional finite element modeling method for electromagnetic calculation of racetrack-shaped superconducting coils according to claim 1 or 2, characterized in that: The electromagnetic calculation equations include but are not limited to: the electric field strength E calculation part with the current vector potential T as the independent variable in the TA formula solution system, the critical current density based on the Kim critical state model J c Calculation part: Nonlinear resistivity based on EJ power law r HTS Calculation part.

6. A three-dimensional finite element modeling method for electromagnetic calculation of racetrack-shaped superconducting coils according to claim 1, characterized in that: The material physical properties include electrical conductivity, magnetic permeability and relative permittivity.

7. A system for three-dimensional finite element modeling of racetrack-shaped superconducting coil electromagnetic calculations, characterized in that: The system comprises: processor; a memory having stored thereon a computer program executable on the processor; Wherein, when the computer program is executed by the processor, the steps of the three-dimensional finite element modeling method for electromagnetic calculation of racetrack-shaped superconducting coils as claimed in any one of claims 1 to 6 are implemented.

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