Superconducting reactor alternating current loss simulation method based on in-situ substitution

Abstract

The invention relates to an in-situ substitution-based superconducting reactor alternating current loss simulation method, which comprises the following steps of: for a reactor structure, substituting other superconducting coils except a superconducting coil winding to be analyzed into regular geometric structures in situ by adopting a finite element method; a single-coil three-dimensional simplified model and a fine model of the reactor structure are constructed, inductance and magnetic field distribution parameters are solved through the single-coil three-dimensional simplified model, boundary conditions are set through the fine model in combination with the obtained inductance and magnetic field distribution parameters, and the reactor structure is obtained. Solving through a Maxwell equation set to obtain an electric field and current density in the superconducting tape; and calculating AC loss power, and calculating the AC loss of the coil winding of the superconducting reactor. Compared with the prior art, the method has the advantages that the efficiency and precision of alternating current loss calculation of the superconducting reactor can be improved, a key basis is provided for design optimization and performance evaluation of the superconducting reactor, and application of the superconducting technology in an electric power system is powerfully promoted.

Description

Technical Field

[0001] The invention relates to the technical field of superconducting reactors, and in particular to a superconducting reactor AC loss simulation method based on in-situ substitution. Background Art

[0002] With the continuous development of power systems, the performance requirements for power equipment are increasing. As a key device in power systems, superconducting reactors play an important role in reactive power compensation and short-circuit current limitation.

[0003] Traditional reactors have certain limitations during operation, such as high loss, high noise, and large footprint, which not only reduces energy efficiency, but also generates excessive heat, affecting the stability and service life of the equipment. The emergence of superconducting technology has brought new opportunities to solve these problems.

[0004] Superconducting materials have the characteristics of zero resistance or extremely low resistance. When superconducting materials are in a superconducting state, they can significantly reduce the loss when current passes through. Among them, the second-generation high-temperature superconducting REBCO tape shows a higher superconducting transition temperature, stronger current carrying capacity and larger irreversible field compared to the first-generation BSCCO tape. This allows it to maintain a large critical current in a high magnetic field environment, and the significant reduction in its raw material costs makes its large-scale application in the field of superconducting reactors economically feasible.

[0005] However, the structure of superconducting reactors is relatively complex, usually composed of multiple double-pancake insulated superconducting coils. There are many challenges in studying and analyzing their performance. The critical current of the superconducting coil is affected by temperature and magnetic field, and the magnetic field and AC loss of irregular coils are asymmetric, which makes calculations extremely difficult. Traditional calculation methods are difficult to accurately simulate the electromagnetic characteristics and AC losses of superconducting reactors in actual work. As an effective numerical calculation method, the finite element method can decompose complex physical systems into multiple tiny mathematical units for solution. However, when applied to superconducting reactors, due to the extremely large width-to-thickness ratio of superconducting tapes, meshing is difficult, and the model is prone to non-convergence, which seriously affects the accuracy and efficiency of the calculation.

[0006] In summary, there is an urgent need for an AC loss simulation method specifically for superconducting reactors, which can fully utilize the advantages of superconducting materials, overcome the calculation difficulties caused by complex structures, and accurately simulate the electromagnetic characteristics and AC losses of superconducting reactors, thereby providing a reliable basis for the design, optimization and performance evaluation of superconducting reactors. This is exactly the technical problem that the present invention is committed to solving. Summary of the invention

[0007] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a superconducting reactor AC loss simulation method based on in-situ substitution. The present invention can improve the efficiency and accuracy of superconducting reactor AC loss calculation, provide a key basis for its design optimization and performance evaluation, and effectively promote the application of superconducting technology in power systems.

[0008] The purpose of the present invention can be achieved by the following technical solutions:

[0009] The present invention provides a method for simulating AC loss of a superconducting reactor based on in-situ substitution, comprising the following steps:

[0010] S1: Using multi-physics finite element simulation software, the finite element method is used for the reactor structure to replace the remaining superconducting coils except the superconducting coil windings to be analyzed with regular geometric structures in situ;

[0011] S2: Based on the simplified results in S1, a three-dimensional simplified model and a refined model of a single coil of the reactor structure are constructed, and the inductance and magnetic field distribution parameters are solved by the three-dimensional simplified model of the single coil. The boundary conditions are set by combining the obtained inductance and magnetic field distribution parameters with the refined model, and the electric field and current density in the superconducting tape are solved by solving the Maxwell equations.

[0012] S3: Integrate the product of the electric field and current density in the superconducting tape obtained in S2 to obtain the AC loss power, and deal with the problem that the power does not reach a steady state under zero initial conditions to calculate the AC loss of the superconducting reactor coil winding.

[0013] Furthermore, S1 specifically includes the following steps:

[0014] S1-1: Based on multi-physics finite element simulation software and the finite element method, the physical system of the superconducting reactor is decomposed into tiny mathematical units for solution;

[0015] S1-2: analyzing the superconducting reactor ring structure, and corresponding the superconducting reactor ring structure to a plurality of superconducting and insulating superconducting coil ring combinations;

[0016] S1-3: For the superconducting coil windings, after selecting the winding to be analyzed, the remaining superconducting coils are replaced in situ.

[0017] Furthermore, S2 specifically includes the following steps:

[0018] S2-1: Construct a simplified three-dimensional model, which treats the coil as a ring conductor without subdividing the number of turns, so as to solve the coil inductance, overall distribution of magnetic field and related parameters;

[0019] S2-2: construct a three-dimensional fine model, wherein the three-dimensional fine model describes the shape of each turn and adds an air domain to be equivalent to an insulated coil, and sets an AC current excitation to the single-phase coil winding of the reactor;

[0020] S2-3: Combine the magnetic field calculated by the simplified model in S1 to set boundary conditions, and perform transient field simulation based on Maxwell's equations to solve the electric field and current density distribution.

[0021] Furthermore, S2-1 specifically includes the following steps:

[0022] According to the actual structure and electromagnetic characteristics of the superconducting reactor, a single coil is abstracted and simplified, and the specific geometric shape and size parameters of the equivalent ring conductor are determined, and a three-dimensional basic model framework is constructed without considering the subdivision of the number of turns.

[0023] For the constructed 3D simplified model framework, appropriate calculation conditions are set according to electromagnetic theory and the functional requirements of simulation software;

[0024] The model is calculated using the solver in the multi-physics field finite element simulation software to obtain the relevant electromagnetic parameters of the coil.

[0025] Furthermore, S2-2 specifically includes the following steps:

[0026] According to the actual number of turns, shape details and relative position relationship between each turn of a single coil of the superconducting reactor, a three-dimensional fine model framework capable of describing the shape of each turn is constructed in the simulation software;

[0027] In the model, an air domain is added to the area between the superconducting tapes to be equivalent to the actual physical state of the insulating coil.

[0028] According to the working principle and simulation requirements of the superconducting reactor, the parameters of the alternating current passed into the single-phase coil winding of the reactor are set, and the parameters of the alternating current include the amplitude, frequency and phase information of the current.

[0029] Furthermore, S2-3 specifically includes the following steps:

[0030] Extracting magnetic field data calculated by the simplified model in S1, the magnetic field data includes magnetic field intensity, magnetic field direction, and distribution information of the magnetic field at different spatial positions, sorting and analyzing the magnetic field data, and determining its corresponding relationship and scope of action in the three-dimensional fine model;

[0031] According to the magnetic field data, appropriate boundary conditions are set for the three-dimensional fine model so that the magnetic field conditions at the model boundary match the calculation results of the S1 simplified model;

[0032] The three-dimensional detailed model with set boundary conditions is substituted into the transient field simulation solution system built based on Maxwell's equations. Taking into account the material properties, geometric structure and applied AC current factors of the model, the Maxwell equations are numerically solved through simulation software, and the electric field and current density distribution of the superconducting tape inside the model during the transient process are gradually iterated and calculated.

[0033] Furthermore, S3 specifically includes the following steps:

[0034] S3-1: Enable the volume integration function in the simulation software, and perform product integration operations on the electric field and current density data in the superconducting tape obtained in S2 according to the pre-set integration area, so as to obtain the preliminary calculation results of the AC loss power of the superconducting tape in one cycle;

[0035] S3-2: Analyze the unstable characteristics of this calculation result under zero initial conditions;

[0036] S3-3: Calculate the approximate AC loss of a single coil winding in steady state;

[0037] S3-4: Based on the number of coil windings in a single phase of the superconducting reactor and the characteristics of its three-phase structure, the total AC loss of the superconducting reactor coil winding is calculated, providing key quantitative indicator basis for the performance evaluation and optimal design of the superconducting reactor.

[0038] Furthermore, S3-1 specifically includes the following steps:

[0039] Enable the volume integration function module in the multi-physics finite element simulation software, extract the electric field and current density data in the superconducting tape from the result data obtained by S2, and import it into the calculation framework of the volume integration function;

[0040] According to the actual physical structure and characteristics of the superconducting tape of the superconducting reactor, set the precise integration area in the simulation software;

[0041] The computing power of the finite element simulation software is used to perform point-by-point multiplication of the electric field and current density data, and integrate them within the set integration area. The integral value within one cycle is gradually accumulated and calculated according to the time step, thereby obtaining a preliminary value of the AC loss power of the superconducting tape within one cycle.

[0042] Furthermore, S3-2 specifically includes the following steps:

[0043] Obtain a data sequence of preliminary calculation results of the AC power loss of the superconducting tape in one cycle obtained in S3-1, visualize the data sequence, and draw a curve of power change over time;

[0044] Based on the theoretical characteristics of electromagnetic systems under zero initial conditions, the expected change law of AC power loss under normal stable conditions is compared, and attention is paid to the fluctuation of the data sequence at the initial stage, that is, in the first half cycle;

[0045] By statistically analyzing the amplitude and frequency of the fluctuations and the degree of difference in the subsequent stable data, the specific manifestation of the unstable characteristics is determined. At the same time, the relationship between the instability phenomenon and the initial electromagnetic state of the superconducting tape, the initial change of the applied excitation, and the transient response of the model boundary conditions at the initial moment is analyzed.

[0046] Furthermore, S3-3 specifically includes the following steps:

[0047] From the AC power loss data sequence analyzed in S3-2, extract the data part within the second half cycle, use the mathematical averaging algorithm to calculate the data of the second half cycle, and get the average AC power loss value within the cycle. This value is the approximate AC loss of a single coil winding in a stable state.

[0048] Furthermore, S3-4 specifically includes the following steps:

[0049] Obtain the exact number of coil windings in a single phase of a superconducting reactor and determine the need to expand the single-phase result by a corresponding multiple;

[0050] The approximate value of the AC loss of a single coil winding in a steady state obtained in S3-3 is multiplied by the number of coil windings in a single phase of the superconducting reactor to obtain the total AC loss of all coil windings in a single phase;

[0051] Then, the total AC loss of the above single-phase is multiplied by the number of phases to calculate the total AC loss value of the superconducting reactor coil winding.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] 1) The present invention adopts the finite element method and combines the method of replacing the superconducting coil of some toroidal reactors in situ with regular geometric structures, which effectively reduces the computational complexity. By constructing a three-dimensional simplified model to solve the coil inductance, overall magnetic field distribution and other parameters, preliminary results can be quickly obtained to provide basic data for subsequent fine calculations and reduce the overall calculation time. At the same time, the three-dimensional fine model can accurately depict the shape of each turn and consider the insulation conditions. After setting the boundary conditions in combination with the simplified model magnetic field data, the transient field simulation is performed according to the Maxwell equations to solve the electric field and current density distribution, which can more accurately simulate the internal electromagnetic conditions of the superconducting reactor, thereby improving the accuracy of AC loss calculation.

[0054] 2) The AC loss data obtained by the method of the present invention can be used to optimize the parameters and structural layout of the superconducting coil in the design stage, such as reasonably selecting superconducting tapes, determining the number of turns and shape of the coil, etc., so as to reduce AC loss and improve the energy efficiency of the superconducting reactor. In terms of performance evaluation, it is possible to judge whether the superconducting reactor meets the actual operation requirements based on accurate AC loss data, evaluate its stability and reliability under different working conditions, and help to timely discover potential problems and make improvements.

[0055] 3) The present invention effectively solves the problem in the simulation calculation of AC loss of superconducting reactors, making the application of superconducting technology in power systems more feasible and reliable. With the optimization and improvement of the performance of superconducting reactors, they can play a better role in key links of power systems such as reactive power compensation and short-circuit current limitation, which helps to improve the operation stability of the entire power system, reduce energy consumption, and improve the quality of electric energy, thereby promoting the power industry to develop in a more efficient and intelligent direction. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a schematic diagram of the structure of a superconducting reactor;

[0057] Figure 2 This is the superconducting coil structure - an enlarged view of the superconducting coil;

[0058] Figure 3 The spatial magnetic field distribution diagram of a single coil is solved, where (a) is a top view and (b) is a side view.

[0059] Figure 4 is the spatial magnetic field distribution diagram;

[0060] Figure 5 is the curve of magnetic field intensity H changing with x;

[0061] Figure 6 It is a schematic diagram of an equivalent insulated coil;

[0062] Figure 7 The equivalent structure diagram of a single phase of a superconducting reactor based on in-situ substitution in a transient model;

[0063] Figure 8 This is a schematic diagram of the target coil current density and electric field distribution of the superconducting reactor at 0.015s;

[0064] Fig. 9 This is the integrated diagram of AC power loss in one cycle of the superconducting tape. DETAILED DESCRIPTION

[0065] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. Component models, material names, connection structures, control methods, algorithms and other features not clearly described in this technical solution are all considered to be common technical features disclosed in the prior art.

[0066] Example 1

[0067] This embodiment provides a method for simulating AC loss of a superconducting reactor based on in-situ substitution, comprising the following steps:

[0068] S1: Using multi-physics finite element simulation software, the finite element method is used for the reactor structure to replace the remaining superconducting coils except the superconducting coil windings to be analyzed with regular geometric structures in situ;

[0069] S1 specifically includes the following steps:

[0070] S1-1: Based on multi-physics finite element simulation software and the finite element method, the physical system of the superconducting reactor is decomposed into tiny mathematical units for solution;

[0071] S1-2: analyzing the superconducting reactor ring structure, and corresponding the superconducting reactor ring structure to a plurality of superconducting and insulating superconducting coil ring combinations;

[0072] S1-3: For the superconducting coil windings, after selecting the winding to be analyzed, the remaining superconducting coils are replaced in situ.

[0073] The above steps of the present invention are intended to reasonably simplify the model structure of the superconducting reactor so as to more efficiently and accurately perform subsequent related analysis and calculation. First, in step S1, multi-physics field finite element simulation software is used and the finite element method is selected because the finite element method can decompose the complex superconducting reactor physical system into many tiny mathematical units according to its physical properties and geometric shapes, and solve and integrate these units separately to achieve the numerical simulation solution of the entire system, which provides a basic calculation framework for subsequent analysis. Then, step S1-2 analyzes the superconducting reactor ring structure and corresponds it to a plurality of superconducting and insulating superconducting coil ring combinations, in order to clearly define the specific composition of the superconducting reactor, understand the arrangement, connection and other relationships between the superconducting coils, so as to accurately grasp the distribution law of its electromagnetic characteristics. Finally, in step S1-3, for the superconducting coil windings, the winding to be analyzed is selected and the remaining superconducting coils are replaced in situ. This is because in actual analysis, it is often necessary to focus on specific windings to be analyzed, and the remaining superconducting coils are replaced in situ with regular geometric structures. This can not only retain the large electromagnetic field distribution characteristics of the overall structure, but also greatly reduce the computational complexity of the model, so that subsequent calculations based on the simplified model (such as solving related parameters in subsequent steps, etc.) can be carried out more efficiently, avoiding problems such as excessive calculation amount, long calculation time, and even difficulty in convergence due to the original complex structure.

[0074] S2: Based on the simplified results in S1, a three-dimensional simplified model and a refined model of a single coil of the reactor structure are constructed, and the inductance and magnetic field distribution parameters are solved by the three-dimensional simplified model of the single coil. The boundary conditions are set by combining the obtained inductance and magnetic field distribution parameters with the refined model, and the electric field and current density in the superconducting tape are solved by solving the Maxwell equations.

[0075] S2 specifically includes the following steps:

[0076] S2-1: Construct a simplified three-dimensional model, which treats the coil as a ring conductor without subdividing the number of turns, so as to solve the coil inductance, overall distribution of magnetic field and related parameters;

[0077] S2-2: construct a three-dimensional fine model, wherein the three-dimensional fine model describes the shape of each turn and adds an air domain to be equivalent to an insulated coil, and sets an AC current excitation to the single-phase coil winding of the reactor;

[0078] S2-3: Combine the magnetic field calculated by the simplified model in S1 to set boundary conditions, and perform transient field simulation based on Maxwell's equations to solve the electric field and current density distribution.

[0079] S2-1 specifically includes the following steps:

[0080] According to the actual structure and electromagnetic characteristics of the superconducting reactor, a single coil is abstracted and simplified, and the specific geometric shape and size parameters of the equivalent ring conductor are determined, and a three-dimensional basic model framework is constructed without considering the subdivision of the number of turns.

[0081] For the constructed 3D simplified model framework, appropriate calculation conditions are set according to electromagnetic theory and the functional requirements of simulation software;

[0082] The model is calculated using the solver in the multi-physics field finite element simulation software to obtain the relevant electromagnetic parameters of the coil.

[0083] S2-2 specifically includes the following steps:

[0084] According to the actual number of turns, shape details and relative position relationship between each turn of a single coil of the superconducting reactor, a three-dimensional fine model framework capable of describing the shape of each turn is constructed in the simulation software;

[0085] In the model, an air domain is added to the area between the superconducting tapes to be equivalent to the actual physical state of the insulating coil.

[0086] According to the working principle and simulation requirements of the superconducting reactor, the parameters of the alternating current passed into the single-phase coil winding of the reactor are set, and the parameters of the alternating current include the amplitude, frequency and phase information of the current.

[0087] S2-3 specifically includes the following steps:

[0088] Extracting magnetic field data calculated by the simplified model in S1, the magnetic field data includes magnetic field intensity, magnetic field direction, and distribution information of the magnetic field at different spatial positions, sorting and analyzing the magnetic field data, and determining its corresponding relationship and scope of action in the three-dimensional fine model;

[0089] According to the magnetic field data, appropriate boundary conditions are set for the three-dimensional fine model so that the magnetic field conditions at the model boundary match the calculation results of the S1 simplified model;

[0090] The three-dimensional detailed model with set boundary conditions is substituted into the transient field simulation solution system built based on Maxwell's equations. Taking into account the material properties, geometric structure and applied AC current factors of the model, the Maxwell equations are numerically solved through simulation software, and the electric field and current density distribution of the superconducting tape inside the model during the transient process are gradually iterated and calculated.

[0091] The principle of the above steps of the present invention is: in step S2, a single coil model of different precisions is constructed based on the simplified result of S1 to analyze the internal electromagnetic conditions of the superconducting reactor. First, a three-dimensional simplified model is constructed in S2-1, which is an abstract simplification based on the actual structure and electromagnetic characteristics of the superconducting reactor. The coil is equivalent to a ring conductor to construct a model framework, and the calculation conditions are set and the software solver is used for calculation. In this way, preliminary electromagnetic parameters such as inductance and overall distribution of magnetic field can be efficiently obtained. Then S2-2 constructs a three-dimensional fine model in order to simulate the actual situation more accurately. By constructing a model framework based on the actual details of the coil, adding an air domain equivalent insulation coil, and setting the parameters of the AC current, a model close to the real working state is created. Finally, in S2-3, by extracting and organizing the magnetic field data of the simplified model of S1, analyzing its relationship with the three-dimensional fine model, setting matching boundary conditions, substituting it into the transient field simulation solution system constructed by the Maxwell equations, comprehensively considering various factors of the model, and using software iterative solution, the transient electric field and current density distribution in the superconducting tape can be accurately obtained. This model construction and parameter solution method from coarse to fine helps to comprehensively and accurately analyze the electromagnetic characteristics of superconducting reactors.

[0092] S3: Integrate the product of the electric field and current density in the superconducting tape obtained in S2 to obtain the AC loss power, and deal with the problem that the power does not reach a steady state under zero initial conditions to calculate the AC loss of the superconducting reactor coil winding.

[0093] S3 specifically includes the following steps:

[0094] S3-1: Enable the volume integration function in the simulation software, and perform product integration operations on the electric field and current density data in the superconducting tape obtained in S2 according to the pre-set integration area, so as to obtain the preliminary calculation results of the AC loss power of the superconducting tape in one cycle;

[0095] S3-2: Analyze the unstable characteristics of this calculation result under zero initial conditions;

[0096] S3-3: Calculate the approximate AC loss of a single coil winding in steady state;

[0097] S3-4: Based on the number of coil windings in a single phase of the superconducting reactor and the characteristics of its three-phase structure, the total AC loss of the superconducting reactor coil winding is calculated, providing key quantitative indicator basis for the performance evaluation and optimal design of the superconducting reactor.

[0098] S3-1 specifically includes the following steps:

[0099] Enable the volume integration function module in the multi-physics finite element simulation software, extract the electric field and current density data in the superconducting tape from the result data obtained by S2, and import it into the calculation framework of the volume integration function;

[0100] According to the actual physical structure and characteristics of the superconducting tape of the superconducting reactor, set the precise integration area in the simulation software;

[0101] The computing power of the finite element simulation software is used to perform point-by-point multiplication of the electric field and current density data, and integrate them within the set integration area. The integral value within one cycle is gradually accumulated and calculated according to the time step, thereby obtaining a preliminary value of the AC loss power of the superconducting tape within one cycle.

[0102] S3-2 specifically includes the following steps:

[0103] Obtain a data sequence of preliminary calculation results of the AC power loss of the superconducting tape in one cycle obtained in S3-1, visualize the data sequence, and draw a curve of power change over time;

[0104] Based on the theoretical characteristics of electromagnetic systems under zero initial conditions, the expected change law of AC power loss under normal stable conditions is compared, and attention is paid to the fluctuation of the data sequence at the initial stage, that is, in the first half cycle;

[0105] By statistically analyzing the amplitude and frequency of the fluctuations and the degree of difference in the subsequent stable data, the specific manifestation of the unstable characteristics is determined. At the same time, the relationship between the instability phenomenon and the initial electromagnetic state of the superconducting tape, the initial change of the applied excitation, and the transient response of the model boundary conditions at the initial moment is analyzed.

[0106] S3-3 specifically includes the following steps:

[0107] From the AC power loss data sequence analyzed in S3-2, extract the data part within the second half cycle, use the mathematical averaging algorithm to calculate the data of the second half cycle, and get the average AC power loss value within the cycle. This value is the approximate AC loss of a single coil winding in a stable state.

[0108] S3-4 specifically includes the following steps:

[0109] Obtain the exact number of coil windings in a single phase of a superconducting reactor and determine the need to expand the single-phase result by a corresponding multiple;

[0110] The approximate value of the AC loss of a single coil winding in a steady state obtained in S3-3 is multiplied by the number of coil windings in a single phase of the superconducting reactor to obtain the total AC loss of all coil windings in a single phase;

[0111] Then, the total AC loss of the above single-phase is multiplied by the number of phases to calculate the total AC loss value of the superconducting reactor coil winding.

[0112] The following is an explanation of the principles of the above steps of the present invention:

[0113] First, in S3-1, based on the function of multi-physics finite element simulation software, the volume integration function module is enabled to process the electric field and current density data in the superconducting tape obtained by S2. By setting the precise integration area according to the actual physical structure and characteristics of the superconducting tape, the software computing power is used to multiply the electric field and current density point by point and integrate them in the area according to the time step. In this way, the cumulative effect of the product of the two in one cycle can be converted into the preliminary calculation result of the AC loss power of the superconducting tape in one cycle according to the electromagnetic principle, laying the foundation for further analysis and calculation.

[0114] Next, S3-2 analyzes the data sequence of the preliminary calculation results obtained in S3-1. The power variation curve is plotted through visual display, and the fluctuations in the first half cycle are focused on based on the comparison between the theoretical characteristics of the electromagnetic system under zero initial conditions and the normal stable state. The unstable characteristics are determined by statistical analysis of fluctuation-related indicators, and their relationship with the initial electromagnetic state of the superconducting tape, the initial changes in excitation, and the initial transient response of the model boundary conditions is analyzed, so as to gain a deeper understanding of the situation when the power does not reach a steady state under zero initial conditions.

[0115] Then, S3-3 obtains the approximate value of the AC loss of a single coil winding in a stable state to solve the instability problem. The data in the second half cycle is extracted from the data sequence analyzed in S3-2, and the average AC loss power value in the cycle is calculated using a suitable mathematical averaging algorithm, which is used as the approximate value of the AC loss of a single coil winding in a stable state, so that a relatively stable part can be found in the unstable overall cycle data to represent the AC loss of a single coil winding when it is working stably.

[0116] Finally, in S3-4, the number of coil windings in the single phase of the superconducting reactor and the characteristics of the three-phase structure are considered. First, the accurate quantity value is obtained and the expansion multiple of the single-phase result is determined. The approximate value of the single coil winding obtained in S3-3 is multiplied by the number of single-phase coil windings to obtain the single-phase sum, and then multiplied by 3 to obtain the total AC loss value of the superconducting reactor coil winding, so as to comprehensively and accurately calculate the total AC loss, providing a key quantitative indicator basis for evaluating the performance of superconducting reactors and optimizing their design, so as to measure their operating effects from the perspective of energy consumption and guide improvements.

[0117] Application Example 1

[0118] The superconducting reactor is composed of multiple racetrack-shaped double-pan insulated superconducting coils. The superconducting coils are all wound with the second-generation high-temperature superconducting REBCO tape. The second-generation high-temperature superconducting REBCO is a rare earth high-temperature superconducting tape. Compared with the first-generation BSCCO tape, it has a higher superconducting transition temperature, current carrying capacity and irreversible field. It can maintain a larger critical current under high magnetic fields, and the raw material cost is greatly reduced, which is very suitable for the use of superconducting reactors.

[0119] The critical current of the superconducting coil is affected by temperature and magnetic field, while the magnetic field and AC loss of the irregular coil are asymmetric and difficult to calculate, so it is necessary to use COMSOL multi-physics finite element simulation analysis software to perform electromagnetic field analysis. The finite element method means: in order to achieve the purpose of simulating a physical system close to reality, a physical system is decomposed into a finite number of tiny mathematical units for solution. Each mathematical unit corresponds to an approximate solution, and then the overall satisfaction conditions of the corresponding physical model are derived and solved, so as to obtain an approximate solution for the entire model. The finer the decomposition, the closer it is to the real physical state, but it is also accompanied by an exponential increase in the amount of calculation. Reasonable meshing to balance accuracy and calculation speed is a point that needs to be carefully weighed.

[0120] For superconducting reactors, since they are composed of multiple racetrack-shaped double-pancake insulated superconducting coils, and each superconducting coil is wound with multiple turns of superconducting tape, the extremely large width-to-thickness ratio of the superconducting tape places higher requirements on meshing. Since the thickness of the superconducting layer is much smaller than the thickness of the insulating layer, it is very easy for the model to not converge, and appropriate geometric simplification is required. Since the toroidal reactor can be regarded as the superposition of multiple separate double-pancake coil windings, for each double-pancake coil winding, the problem can be parallelized, and only the superconducting characteristics of the double-pancake coil are introduced. The remaining double-pancake coils are replaced in situ with regular geometric structures, and only the magnetic field generated by the remaining double-pancake coils is considered, which reduces the difficulty of calculation. Figure 1 is a schematic diagram of the superconducting reactor structure. Figure 2 This is the superconducting coil structure - an enlarged view of the superconducting coil.

[0121] (1) Single coil simplified model and magnetic field simulation calculation

[0122] In this application example, the simplified three-dimensional model of a single coil treats the coil as an equivalent annular conductor without subdividing the number of turns inside. This sacrifices some accuracy but makes the mesh easy to divide and has a fast calculation speed. It is suitable for preliminary solutions to the overall distribution of the coil inductance and magnetic field, but cannot solve the electric field distribution of the coil. Figure 3The figure is a simplified three-dimensional model geometry of a single coil, (a) is a top view, and (b) is a side view. In this model, the length of the straight segment of the conductor is 0.1m, the inner diameter of the arc segment is 0.18m, the thickness of a single pancake is 4.8mm, and the width is approximately 151 (turns) × 0.42 (mm). When a current of 20.4 (A) × 151 (turns) is applied to a single conductor, the distribution of the spatial magnetic field, inductance, and critical current can be solved. Figure 3 is the spatial magnetic field distribution diagram of a single coil, (a) top view, (b) side view, Figure 4 This is a spatial magnetic field distribution diagram.

[0123] In this application example, a plane z=0 is intercepted along the middle symmetry axis of the coil, and a curve of the magnetic field intensity H changing with x on the intersection of the planes z=0 and y=0 is plotted, as shown in FIG. Figure 5 , x=0.4 is the magnetic field strength at the center point, which is about 16mT.

[0124] (2) Single coil detailed model and electric field simulation

[0125] In this application example, to calculate the electric field and AC loss of the coil, a three-dimensional fine model of a single coil is needed to depict the shape of each turn of the coil, which has a higher solution accuracy. The dielectric properties of the superconducting tape insulation material are equivalent to air, so an air domain is added between the superconducting tape and the superconducting tape to be equivalent to an insulating coil, such as Figure 6 shown.

[0126] In this application example, for Figure 7 The superconducting coil (blue) whose AC loss is to be calculated first passes an AC current I=I into the single-phase coil winding of the reactor. peak sin(2πft), calculate the magnetic field B of other coils at this point according to the first step, and then set the boundary conditions of the magnetic field B and current I based on the three-dimensional fine model of a single coil in the figure above, and perform transient field simulation and solution for the electric field and current density distribution of the coil winding according to Maxwell's equations.

[0127] (3) AC loss calculation

[0128] Figure 8 The diagram is a schematic diagram of the target coil current density and electric field distribution at 0.015s of the superconducting reactor. In this application example, the volume integral function in the derived value is selected to integrate the product of the electric field and current density (mfh.normJ*mfh.normE) in the superconducting tape to obtain the AC loss power in one cycle of the superconducting tape, such as Fig. 9As shown. Due to the existence of zero initial conditions, the calculation results are not stable in the first half cycle. The AC loss power of the second half cycle is averaged to obtain the AC loss of a single coil winding, which is then multiplied by the number of coil windings M in a single phase of the toroidal reactor and then multiplied by 3 (three-phase) to obtain the total AC loss P of the superconducting shunt reactor.

[0129]

[0130] The above description of the embodiments is to facilitate the understanding and use of the invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to these embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments, and improvements and modifications made by those skilled in the art based on the disclosure of the present invention without departing from the scope of the present invention should be within the scope of protection of the present invention.

Claims

1. A method for simulating AC loss of a superconducting reactor based on in-situ substitution, characterized in that: The following steps are involved: S1: Using multi-physics finite element simulation software, the finite element method is used for the reactor structure to replace the remaining superconducting coils except the superconducting coil windings to be analyzed with regular geometric structures in situ; S2: Based on the simplified results in S1, a three-dimensional simplified model and a refined model of a single coil of the reactor structure are constructed, and the inductance and magnetic field distribution parameters are solved by the three-dimensional simplified model of the single coil. The boundary conditions are set by combining the obtained inductance and magnetic field distribution parameters with the refined model, and the electric field and current density in the superconducting tape are solved by solving the Maxwell equations. S3: Integrate the product of the electric field and current density in the superconducting tape obtained in S2 to obtain the AC loss power, and deal with the problem that the power does not reach a steady state under zero initial conditions to calculate the AC loss of the superconducting reactor coil winding.

2. The method for simulating AC loss of a superconducting reactor based on in-situ substitution according to claim 1, characterized in that: S1 specifically includes the following steps: S1-1: Based on multi-physics finite element simulation software and the finite element method, the physical system of the superconducting reactor is decomposed into tiny mathematical units for solution; S1-2: analyzing the superconducting reactor ring structure, and corresponding the superconducting reactor ring structure to a plurality of superconducting and insulating superconducting coil ring combinations; S1-3: For the superconducting coil windings, after selecting the winding to be analyzed, the remaining superconducting coils are replaced in situ.

3. The method for simulating AC loss of a superconducting reactor based on in-situ substitution according to claim 1, characterized in that: S2 specifically includes the following steps: S2-1: Construct a simplified three-dimensional model, which treats the coil as a ring conductor without subdividing the number of turns, so as to solve the coil inductance, overall distribution of magnetic field and related parameters; S2-2: construct a three-dimensional fine model, wherein the three-dimensional fine model describes the shape of each turn and adds an air domain to be equivalent to an insulated coil, and sets an AC current excitation to the single-phase coil winding of the reactor; S2-3: Combine the magnetic field calculated by the simplified model in S1 to set boundary conditions, and perform transient field simulation based on Maxwell's equations to solve the electric field and current density distribution.

4. The method for simulating AC loss of a superconducting reactor based on in-situ substitution according to claim 3, characterized in that: S2-1 specifically includes the following steps: According to the actual structure and electromagnetic characteristics of the superconducting reactor, a single coil is abstracted and simplified, and the specific geometric shape and size parameters of the equivalent ring conductor are determined, and a three-dimensional basic model framework is constructed without considering the subdivision of the number of turns. For the constructed 3D simplified model framework, appropriate calculation conditions are set according to electromagnetic theory and the functional requirements of simulation software; The solver in the multi-physics finite element simulation software is used to calculate the model, thereby obtaining the relevant electromagnetic parameters of the coil; S2-2 specifically includes the following steps: According to the actual number of turns, shape details and relative position relationship between each turn of a single coil of the superconducting reactor, a three-dimensional fine model framework capable of describing the shape of each turn is constructed in the simulation software; In the model, an air domain is added to the area between the superconducting tapes to be equivalent to the actual physical state of the insulating coil. According to the working principle and simulation requirements of the superconducting reactor, the parameters of the alternating current passed into the single-phase coil winding of the reactor are set, and the parameters of the alternating current include the amplitude, frequency and phase information of the current.

5. The method for simulating AC loss of a superconducting reactor based on in-situ substitution according to claim 3, characterized in that: S2-3 specifically includes the following steps: Extracting magnetic field data calculated by the simplified model in S1, the magnetic field data includes magnetic field intensity, magnetic field direction, and distribution information of the magnetic field at different spatial positions, sorting and analyzing the magnetic field data, and determining its corresponding relationship and scope of action in the three-dimensional fine model; According to the magnetic field data, appropriate boundary conditions are set for the three-dimensional fine model so that the magnetic field conditions at the model boundary match the calculation results of the S1 simplified model; The three-dimensional detailed model with set boundary conditions is substituted into the transient field simulation solution system built based on Maxwell's equations. Taking into account the material properties, geometric structure and applied AC current factors of the model, the Maxwell equations are numerically solved through simulation software, and the electric field and current density distribution of the superconducting tape inside the model during the transient process are gradually iterated and calculated.

6. The method for simulating AC loss of a superconducting reactor based on in-situ substitution according to claim 1, characterized in that: S3 specifically includes the following steps: S3-1: Enable the volume integration function in the simulation software, and perform product integration operations on the electric field and current density data in the superconducting tape obtained in S2 according to the pre-set integration area, so as to obtain the preliminary calculation results of the AC loss power of the superconducting tape in one cycle; S3-2: Analyze the unstable characteristics of this calculation result under zero initial conditions; S3-3: Calculate the approximate AC loss of a single coil winding in steady state; S3-4: Based on the number of coil windings in a single phase of the superconducting reactor and the characteristics of its three-phase structure, the total AC loss of the superconducting reactor coil winding is calculated, providing key quantitative indicator basis for the performance evaluation and optimal design of the superconducting reactor.

7. The method for simulating AC loss of a superconducting reactor based on in-situ substitution according to claim 6, characterized in that: S3-1 specifically includes the following steps: Enable the volume integration function module in the multi-physics finite element simulation software, extract the electric field and current density data in the superconducting tape from the result data obtained by S2, and import it into the calculation framework of the volume integration function; According to the actual physical structure and characteristics of the superconducting tape of the superconducting reactor, set the precise integration area in the simulation software; The computing power of the finite element simulation software is used to perform point-by-point multiplication of the electric field and current density data, and integrate them within the set integration area. The integral value within one cycle is gradually accumulated and calculated according to the time step, thereby obtaining a preliminary value of the AC loss power of the superconducting tape within one cycle.

8. The method for simulating AC loss of a superconducting reactor based on in-situ substitution according to claim 6, characterized in that: S3-2 specifically includes the following steps: Obtain a data sequence of preliminary calculation results of the AC power loss of the superconducting tape in one cycle obtained in S3-1, visualize the data sequence, and draw a curve of power change over time; Based on the theoretical characteristics of electromagnetic systems under zero initial conditions, the expected change law of AC power loss under normal stable conditions is compared, and attention is paid to the fluctuation of the data sequence at the initial stage, that is, in the first half cycle; By statistically analyzing the amplitude and frequency of the fluctuations and the degree of difference in the subsequent stable data, the specific manifestation of the unstable characteristics is determined. At the same time, the relationship between the instability phenomenon and the initial electromagnetic state of the superconducting tape, the initial change of the applied excitation, and the transient response of the model boundary conditions at the initial moment is analyzed.

9. The method for simulating AC loss of a superconducting reactor based on in-situ substitution according to claim 6, characterized in that: S3-3 specifically includes the following steps: From the AC power loss data sequence analyzed in S3-2, extract the data part within the second half cycle, use the mathematical averaging algorithm to calculate the data of the second half cycle, and get the average AC power loss value within the cycle. This value is the approximate AC loss of a single coil winding in a stable state.

10. The method for simulating AC loss of a superconducting reactor based on in-situ substitution according to claim 6, characterized in that: S3-4 specifically includes the following steps: Obtain the exact number of coil windings in a single phase of a superconducting reactor and determine the need to expand the single-phase result by a corresponding multiple; The approximate value of the AC loss of a single coil winding in a steady state obtained in S3-3 is multiplied by the number of coil windings in a single phase of the superconducting reactor to obtain the total AC loss of all coil windings in a single phase; Then, the total AC loss of the above single-phase is multiplied by the number of phases to calculate the total AC loss value of the superconducting reactor coil winding.

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