An in-situ replacement-based simulation method for ac loss of superconducting reactor

Abstract

The application relates to a superconducting reactor AC loss simulation method based on in-situ replacement, which comprises the following steps: for the reactor structure, a finite element method is used to replace the remaining superconducting coils except the superconducting coil winding to be analyzed into regular geometric structures in situ; a single coil three-dimensional simplified model and a fine model of the reactor structure are constructed, the inductance and magnetic field distribution parameters are solved through the single coil three-dimensional simplified model, the obtained inductance and magnetic field distribution parameters are combined, boundary conditions are set, the electric field and current density in the superconducting tape are solved through Maxwell equations, AC loss power is calculated, and the AC loss of the superconducting reactor coil winding is calculated. Compared with the prior art, the application can improve the efficiency and precision of the superconducting reactor AC loss calculation, provides a key basis for design optimization and performance evaluation, and effectively promotes the application of superconducting technology in the power system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of superconducting reactors, in particular to a superconducting reactor AC loss simulation method based on in-situ replacement. BACKGROUND

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

[0003] Traditional reactors have certain limitations in the running process, such as large loss, high noise, and large floor area, which not only reduces the energy utilization efficiency, but also generates excessive heat, affecting the stability and service life of the equipment. The emergence of superconducting technology brings new opportunities to solve these problems.

[0004] Superconducting materials have the characteristics of zero resistance or extremely low resistance. When the superconducting material is in a superconducting state, it can significantly reduce the loss when the current passes through. Among them, the second-generation high-temperature superconducting REBCO tape exhibits 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 larger critical current in a high magnetic field environment, and its raw material cost is greatly reduced, making 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-pie insulated superconducting coil rings. When studying and analyzing its performance, many challenges are faced. 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, making the calculation extremely difficult. Traditional calculation methods are difficult to accurately simulate the electromagnetic characteristics and AC loss of superconducting reactors in actual work. Although the finite element method, as an effective numerical calculation method, can decompose complex physical systems into multiple small mathematical units for solution, when applied to superconducting reactors, due to the extremely large width-to-thickness ratio of superconducting tapes, mesh division is difficult, and the model is prone to divergence, seriously affecting 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 that can fully utilize the advantages of superconducting materials, overcome the calculation difficulties brought by complex structure, and accurately simulate the electromagnetic characteristics and AC loss of superconducting reactors, thereby providing reliable basis for the design, optimization and performance evaluation of superconducting reactors, which is the technical problem that the present application aims to solve. SUMMARY

[0007] The present application aims to overcome the defects of the prior art, and provides an in-situ replacement-based superconducting reactor AC loss simulation method, which can improve the efficiency and accuracy of superconducting reactor AC loss calculation, provide key basis for design optimization and performance evaluation, and effectively promote the application of superconducting technology in power systems.

[0008] The object of the present application can be achieved by the following technical solutions:

[0009] The present application provides an in-situ replacement-based superconducting reactor AC loss simulation method, comprising the following steps:

[0010] S1: using a multi-physics finite element simulation software, for the reactor structure, using the finite element method, replacing the remaining superconducting coils except the superconducting coil winding to be analyzed with a regular geometric structure in-situ;

[0011] S2: based on the simplified results in S1, constructing a single coil three-dimensional simplified model and a fine model of the reactor structure, solving the inductance and magnetic field distribution parameters through the single coil three-dimensional simplified model, setting boundary conditions through the fine model and combining the obtained inductance and magnetic field distribution parameters, and solving the electric field and current density in the superconducting tape through Maxwell equations;

[0012] S3: multiplying the electric field and current density in the superconducting tape obtained in S2 to obtain the AC loss power, processing the problem of power not reaching steady state under zero initial condition, and calculating the AC loss of the superconducting reactor coil winding.

[0013] Further, in S1, the following steps are specifically included:

[0014] S1-1: based on the multi-physics finite element simulation software and selecting the finite element method, the superconducting reactor physical system is divided into small mathematical units for solving;

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

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

[0017] Further, in S2, the following steps are specifically included:

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

[0019] S2-2: constructing a three-dimensional fine model, the three-dimensional fine model depicting each turn shape and adding an air domain to be equivalent to an insulated coil, setting an excitation of an alternating current through a single-phase coil winding of the reactor;

[0020] S2-3: combining the magnetic field set by the simplified model calculation in S1, performing a transient field simulation to solve the electric field and current density distribution according to Maxwell's equations.

[0021] Further, in S2-1, the following steps are specifically included:

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

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

[0024] 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.

[0025] Further, in S2-2, the following steps are specifically included:

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

[0027] Air domains are added in the model corresponding to the superconducting tapes and the regions between the superconducting tapes, to equivalently simulate the actual physical state of the insulated coil;

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

[0029] Further, in S2-3, the following steps are specifically included:

[0030] The magnetic field data obtained by the simplified model calculation in S1 is extracted, including the magnetic field strength, magnetic field direction and distribution information of the magnetic field at different spatial positions, the magnetic field data is sorted and analyzed to determine its corresponding relationship and action range 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 simplified model in S1;

[0032] The three-dimensional fine model with the set boundary condition is substituted into a transient field simulation solving system constructed based on Maxwell equations, and the Maxwell equations are solved by simulation software based on the factors of material properties, geometric structure and applied alternating current of the model, so that the distribution of electric field and current density of the superconducting tape in the model in the transient process is calculated by iterative calculation.

[0033] Further, S3 specifically comprises the following steps:

[0034] S3-1: enabling a volume integral function in the simulation software, and performing product integral operation on the electric field and current density data in the superconducting tape obtained in S2 according to the pre-set integral region, so as to obtain the preliminary calculation result of the alternating loss power of the superconducting tape in one cycle;

[0035] S3-2: analyzing the unstable characteristics of the calculation result under zero initial condition;

[0036] S3-3: calculating the approximate value of the alternating loss of a single coil winding in a stable state;

[0037] S3-4: calculating the total alternating loss of the coil winding of the superconducting reactor according to the number of coil windings in a single phase of the superconducting reactor and the characteristics of the three-phase structure, so as to provide a key quantitative index basis for performance evaluation and optimal design of the superconducting reactor.

[0038] Further, S3-1 specifically comprises the following steps:

[0039] Enabling a volume integral function module in the multi-physical field finite element simulation software, extracting the electric field and current density data in the superconducting tape from the result data obtained in S2, and importing them into the operation framework of the volume integral function;

[0040] According to the actual physical structure and characteristics of the superconducting tape of the superconducting reactor, the accurate integral region is set in the simulation software;

[0041] The calculation capacity of the finite element simulation software is used to perform point-by-point product operation on the electric field and current density data, and to perform integration in the set integral region, and to gradually accumulate the integral value in one cycle according to the time step, so as to obtain the preliminary numerical value of the alternating loss power of the superconducting tape in one cycle.

[0042] Further, S3-2 specifically comprises the following steps:

[0043] Obtaining the preliminary calculation result data sequence of the alternating loss power of the superconducting tape in one cycle obtained in S3-1, visualizing the data sequence, and drawing a curve of power change with time;

[0044] According to the theoretical characteristics of the electromagnetic system under the zero initial condition, the expected change rule of the alternating current loss power under the normal stable state is compared, and the fluctuation of the data sequence in the initial stage, that is, the first half cycle, is focused on;

[0045] By statistically analyzing the amplitude, frequency and difference degree index of the subsequent stable part data of the fluctuation, the specific manifestation form of the unstable characteristics is determined, and the relationship between the unstable 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 condition at the initial moment is analyzed.

[0046] Further, in S3-3, the following steps are specifically included:

[0047] From the alternating current loss power data sequence obtained by analysis in S3-2, the data part in the second half cycle is extracted, and the mathematical average algorithm is used to calculate the second half cycle data to obtain the average alternating current loss power value in the cycle, which is the approximate value of the alternating current loss of the single coil winding in the stable state.

[0048] Further, in S3-4, the following steps are specifically included:

[0049] The accurate number value of the coil winding in the single phase of the superconducting reactor is obtained, and it is determined that the results of the single phase need to be expanded by a corresponding multiple;

[0050] The approximate value of the alternating current loss of the single coil winding in the stable state obtained in S3-3 is multiplied by the number of coil windings in the single phase of the superconducting reactor to obtain the total alternating current loss of all coil windings in the single phase.

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

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

[0053] 1) The present application adopts the finite element method and combines the replacement of the partial superconducting coil of the ring reactor with a regular geometric structure, which effectively reduces the calculation complexity. By constructing a three-dimensional simplified model to solve the coil inductance, magnetic field overall distribution and other parameters, the preliminary results can be quickly obtained, which provides basic data for subsequent fine calculation and reduces 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 condition. After setting the boundary conditions in combination with the magnetic field data of the simplified model, the transient field simulation is carried out according to the Maxwell equations to solve the electric field and current density distribution, which can more accurately simulate the internal electromagnetic situation of the superconducting reactor, thereby improving the accuracy of the alternating current loss calculation.

[0054] 2) The AC loss data obtained by the method of the application can be used to optimize and adjust the parameters and structural layout of the superconducting coil in the design stage, such as reasonably selecting the superconducting tape, determining the number of turns and shape of the coil, etc., to reduce the AC loss and improve the energy utilization efficiency of the superconducting reactor. In terms of performance evaluation, the accuracy of the AC loss data can be used to determine whether the superconducting reactor meets the actual operation requirements, evaluate its stability and reliability under different working conditions, and help to find potential problems and improve them in time.

[0055] 3) The application effectively solves the problem of AC loss simulation calculation 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 more outstanding 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, improve power quality, and thus promote the development of the power industry towards higher efficiency and intelligence. BRIEF DESCRIPTION OF DRAWINGS

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

[0057] Figure 2 is a superconducting coil structure - superconducting coil enlarged view;

[0058] Figure 3 is a spatial magnetic field distribution diagram of a single coil, wherein (a) is a top view and (b) is a side view;

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

[0060] Figure 5 is a curve of magnetic field strength H versus x;

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

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

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

[0064] Figure 9 is an AC loss power integration diagram of a superconducting tape in one period. DETAILED DESCRIPTION

[0065] The present application will be described in detail below in conjunction with the accompanying drawings and specific embodiments. In the technical solution, components, material names, connection structures, control methods, algorithms and other features not explicitly described are considered as common technical features disclosed in the prior art.

[0066] Embodiment 1

[0067] The embodiment provides an in-situ replacement-based AC loss simulation method of a superconducting reactor, comprising the following steps:

[0068] S1: using a multi-physics finite element simulation software, for the reactor structure, using the finite element method, replacing the remaining superconducting coils except the superconducting coil winding to be analyzed with a regular geometric structure in-situ;

[0069] In S1, the following steps are specifically included:

[0070] S1-1: based on the multi-physics finite element simulation software and selecting the finite element method, decomposing the superconducting reactor physical system into a small mathematical unit for solving;

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

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

[0073] The above steps of the present application are aimed at simplifying the model structure of the superconducting reactor in a reasonable manner, so as to more efficiently and accurately perform subsequent related analysis and calculation. Firstly, in the S1 step, the multi-physical field finite element simulation software is utilized and the finite element method is selected, because the finite element method can decompose the complex superconducting reactor physical system into numerous small mathematical units according to the physical characteristics and geometric shapes of the system, solve these units respectively and synthesize them, so as to realize the numerical simulation solution of the whole system, which provides a basic calculation framework for subsequent analysis. Then, in the S1-2 step, the superconducting reactor ring structure is analyzed and corresponded to a plurality of superconducting insulated superconducting coil ring combinations, so as to clearly and explicitly understand the specific form of the superconducting reactor, understand the arrangement, connection and other relationships between the superconducting coils, so as to accurately grasp the distribution law of the electromagnetic characteristics. Finally, in the S1-3 step, for the superconducting coil winding, the winding to be analyzed is selected and the remaining superconducting coils are replaced in situ, which is considered that in actual analysis, only the specific winding to be analyzed needs to be focused on, and the remaining superconducting coils are replaced in situ as regular geometric structures, which can not only retain the general electromagnetic field distribution characteristics of the overall structure, but also greatly reduce the calculation complexity of the model, so that the subsequent calculation based on the simplified model (such as solving related parameters in subsequent steps) can be more efficiently performed, and problems such as excessive calculation amount, excessive calculation time and even difficulty in convergence caused by the original complex structure can be avoided.

[0074] S2: based on the simplified results in S1, constructing a single coil three-dimensional simplified model and a fine model of the reactor structure, solving the inductance and magnetic field distribution parameters through the single coil three-dimensional simplified model, setting boundary conditions through the fine model and the obtained inductance and magnetic field distribution parameters, and solving the electric field and current density in the superconducting tape through Maxwell equations;

[0075] In S2, the following steps are specifically included:

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

[0077] S2-2: constructing a three-dimensional fine model, which depicts the shape of each turn and adds an air domain to equivalently have an insulated coil, and sets the single-phase coil winding of the reactor to be excited by an alternating current;

[0078] S2-3: setting boundary conditions in combination with the magnetic field calculated by the simplified model in S1, and solving the electric field and current density distribution through transient field simulation according to Maxwell equations.

[0079] In S2-1, the following steps are specifically included:

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

[0081] For the constructed three-dimensional simplified model framework, appropriate calculation conditions are set according to electromagnetic theory and functional requirements of the simulation software.

[0082] The model is calculated by using a solver in the multi-physical field finite element simulation software, so as to obtain related 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 turns of the superconducting reactor single coil, a three-dimensional fine model framework capable of depicting the shape of each turn is constructed in the simulation software.

[0085] Air domains are added in the model corresponding to the superconducting tapes and the regions between the superconducting tapes, so as to equivalently simulate the actual physical state of the insulated coil.

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

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

[0088] The magnetic field data obtained by the simplified model calculation in S1 are extracted, the magnetic field data include magnetic field strength, magnetic field direction and distribution information of the magnetic field at different spatial positions, the magnetic field data are arranged and analyzed to determine the corresponding relationship and action range 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 are matched with the calculation results of the simplified model in S1.

[0090] The three-dimensional fine model with the set boundary conditions is substituted into the transient field simulation solution system based on Maxwell's equations, the material properties, geometric structure and applied alternating current factors of the model are considered, and the Maxwell's equations are numerically solved by the simulation software, so as to iteratively calculate the electric field and current density distribution of the superconducting tape in the transient process.

[0091] The principle of the above steps of the present application is that: in the S2 step, based on the simplified results of S1, a single coil model of different accuracy is constructed for analyzing the internal electromagnetic situation of the superconducting reactor. Firstly, a three-dimensional simplified model is constructed in S2-1, which is abstracted and simplified according to the actual structure and electromagnetic characteristics of the superconducting reactor, the coil is equivalent to a ring conductor to construct the model framework, and the software solver is used to calculate after setting the calculation conditions, so that the preliminary electromagnetic parameters such as inductance and overall magnetic field distribution can be efficiently obtained. Then, in S2-2, a three-dimensional fine model is constructed, which is to more accurately simulate the actual situation, the model framework is constructed according to the actual details of the coil, the air domain is added to equivalent the insulating coil, and the parameters of the input alternating current are set to create a model close to the real working state. Finally, in S2-3, the magnetic field data of the S1 simplified model is extracted and arranged, the relationship with the three-dimensional fine model is analyzed, the matching boundary conditions are set, the transient field simulation solving system is constructed by substituting into Maxwell equations, various factors of the model are considered, and the software is iteratively solved, so that the transient electric field and current density distribution in the superconducting tape are accurately obtained. This model construction and parameter solving method from coarse to fine helps to comprehensively and accurately analyze the electromagnetic characteristics of the superconducting reactor.

[0092] S3: The product integral of the electric field and the current density in the superconducting tape obtained in S2 is integrated to obtain the alternating current loss power, and the problem of unstable power under zero initial condition is handled to calculate the alternating current loss of the superconducting reactor coil winding.

[0093] In S3, the following steps are specifically included:

[0094] S3-1: In the simulation software, the volume integral function is enabled, the electric field and current density data in the superconducting tape obtained in S2 are multiplied and integrated according to the pre-set integral region, so as to obtain the preliminary calculation result of the alternating current loss power of the superconducting tape in one period;

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

[0096] S3-3: Calculate the approximate value of the alternating current loss of the single coil winding under stable state;

[0097] S3-4: According to the number of coil windings in the single phase of the superconducting reactor and the characteristics of the three-phase structure, the total alternating current loss of the superconducting reactor coil winding is calculated, which provides a key quantitative index basis for performance evaluation and optimization design of the superconducting reactor.

[0098] In S3-1, the following steps are specifically included:

[0099] Enabling the volume integral function module in the multi-physical field finite element simulation software, extracting the electric field and current density data in the superconducting tape from the result data obtained from S2, and importing them into the operation framework of the volume integral function;

[0100] According to the actual physical structure and characteristics of the superconducting tape of the superconducting reactor, the accurate integral region is set in the simulation software;

[0101] Using the calculation capability of the finite element simulation software, the point-by-point multiplication operation is performed on the electric field and current density data, and the integral is performed in the set integral region. The integral value in a period is gradually accumulated according to the time step, so as to obtain the preliminary numerical value of the alternating current loss power of the superconducting tape in a period.

[0102] In S3-2, the following steps are specifically included:

[0103] The preliminary calculation result data sequence of the alternating current loss power of the superconducting tape in a period obtained in S3-1 is obtained, and the data sequence is visually displayed, and a curve of power changing with time is drawn;

[0104] According to the theoretical characteristics of the electromagnetic system under zero initial condition, the expected change rule of the alternating current loss power under normal stable state is compared, and the fluctuation of the data sequence in the initial stage, i.e. the first half cycle, is focused on;

[0105] By statistically analyzing the amplitude, frequency and difference degree index of the subsequent stable part data of the fluctuation, the specific manifestation form of the unstable characteristics is determined, and the relationship between the unstable 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 condition at the initial moment is analyzed.

[0106] In S3-3, the following steps are specifically included:

[0107] From the alternating current loss power data sequence analyzed in S3-2, the data part in the second half cycle is extracted, and the mathematical average algorithm is used to calculate the second half cycle data to obtain the average alternating current loss power value in the cycle. This value is the approximate value of the alternating current loss of the single coil winding in the stable state.

[0108] In S3-4, the following steps are specifically included:

[0109] The accurate number value of the coil winding in the single phase of the superconducting reactor is obtained, and it is determined that the results of the single phase need to be expanded by a corresponding multiple;

[0110] The approximate value of the alternating current loss of the single coil winding in the stable state obtained in S3-3 is multiplied by the number of coil windings in the single phase of the superconducting reactor to obtain the total alternating current loss of all coil windings in the single phase.

[0111] The total AC loss value of the superconducting reactor coil winding is calculated by multiplying the sum of the above single-phase AC losses by the number of phases.

[0112] The following is a description of the above-mentioned step principles of the present application:

[0113] First, in S3-1, based on the functions of the multi-physical field finite element simulation software, a volume integral function module is enabled to process the electric field and current density data of the superconducting tape obtained in S2. By setting an accurate integration region according to the actual physical structure and characteristics of the superconducting tape, the software calculates the point-by-point product of the electric field and the current density and integrates it in the region by time step, which can convert the cumulative effect of the product of the two in a period into a preliminary calculation result of the AC loss power of the superconducting tape in a period according to electromagnetic principles, laying a foundation for further analysis and calculation.

[0114] Next, S3-2 analyzes the preliminary calculation result data sequence obtained in S3-1. By visualizing and drawing the power-time curve, comparing the theoretical characteristics of the electromagnetic system under zero initial conditions with the normal steady state, and focusing on the fluctuations in the first half cycle, the unstable characteristics are determined by statistical analysis of the fluctuation-related indicators, and the relationship between the initial electromagnetic state of the superconducting tape, the initial change of excitation, and the initial transient response of the model boundary conditions is analyzed to better understand the situation when the power is not in a steady state under zero initial conditions.

[0115] Then, S3-3 obtains an approximate value of the AC loss of a single coil winding in a steady 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 this period is calculated using a suitable mathematical averaging algorithm, which is used as an approximate value of the AC loss of a single coil winding in a steady state, so that a relatively stable part can be found in the overall period of unstable data to represent the AC loss of a single coil winding in a steady state.

[0116] Finally, in S3-4, the number of coil windings in a single phase of the superconducting reactor and the three-phase structure characteristics are considered. The accurate number value is obtained and the expansion multiple of the single-phase result is determined, the approximate value of a single coil winding obtained in S3-3 is multiplied by the number of single-phase coil windings to obtain the total sum in a single phase, and then multiplied by 3 to obtain the total AC loss of the superconducting reactor coil winding, thereby comprehensively and accurately calculating the total AC loss, providing key quantitative index basis for evaluating the performance of the superconducting reactor and optimizing its design, so as to measure its operation effect from the energy consumption angle and guide improvement.

[0117] Application Example 1

[0118] The superconducting reactor is composed of multiple runway-shaped double-pie insulated superconducting coils. The superconducting coils are all wound by second-generation high-temperature superconducting REBCO tapes. The second-generation high-temperature superconducting REBCO is a rare earth high-temperature superconducting tape, which has a higher superconducting transition temperature, current-carrying capacity and irreversible field than the first-generation BSCCO tape, can maintain a larger critical current in a high magnetic field, and has a greatly reduced raw material cost, which is very suitable for the use scenario of the superconducting reactor.

[0119] The critical current of the superconducting coil is affected by temperature and magnetic field, and the magnetic field and alternating current loss of the irregular coil are asymmetric and difficult to calculate, so the COMSOL multi-physics finite element simulation analysis software is used for electromagnetic field analysis. The finite element method refers to: in order to achieve the purpose of simulating a physical system close to reality, a physical system is divided into a finite number of small mathematical units for solving, each mathematical unit corresponds to an approximate solution, and then the total solution of the corresponding physical model is derived to meet the conditions, thereby obtaining the approximate solution of the entire model. The finer the decomposition, the closer to the real physical state, but it is accompanied by an exponential increase in computing capacity. Reasonable meshing needs to balance accuracy and computing speed.

[0120] For the superconducting reactor, since the superconducting reactor is composed of multiple runway-shaped double-pie insulated superconducting coils, and each superconducting coil is wound by multiple turns of superconducting tapes. The superconducting tapes have a large width-to-thickness ratio, which puts higher requirements on meshing. Because the thickness of the superconducting layer is much smaller than that of the insulating layer, the model is prone to divergence, and appropriate geometric simplification is needed. Since the toroidal reactor can be regarded as the superposition of multiple individual double-pie coil windings, for each double-pie coil winding, the problem can be parallelized, only the superconducting properties of the double-pie coil are introduced, the remaining double-pie coils are replaced with regular geometric structures in place, and only the magnetic field generated by the remaining double-pie coils is considered, thereby reducing the difficulty of calculation. Figure 1 Fig. 1 is a structural schematic diagram of a superconducting reactor, Figure 2 Fig. 2 is a structure of a superconducting coil - an enlarged view of a superconducting coil.

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

[0122] In this application example, the three-dimensional simplified model of a single coil is equivalent to a ring-shaped conductor without subdividing the number of turns inside, sacrificing some accuracy but the mesh is easy to subdivide, has very fast calculation speed, and is suitable for preliminary solution of the overall distribution of coil inductance and magnetic field, but cannot solve the electric field distribution of the coil. Figure 3is the three-dimensional simplified model geometry of a single coil, (a) is a top view, (b) is a side view. In this model, the straight conductor segments are 0.1m long, the circular arc segments have an inner diameter of 0.18m, the thickness of a single pancake is 4.8mm, and the width is approximately 151(turns) x 0.42(mm). A current of 20.4(A) x 151(turns) is applied to the single conductor, and the spatial magnetic field distribution, inductance, and critical current can be solved. Figure 3 is the solved spatial magnetic field distribution of a single coil, (a) is a top view, (b) is a side view, Figure 4 is the spatial magnetic field distribution.

[0123] In this application example, the plane z=0 is taken along the middle symmetry axis of the coil, and the curve of the magnetic field strength H on the intersection line of the z=0 and y=0 planes with respect to x is drawn, as shown in Figure 5 , x=0.4 is the center point magnetic field strength, which is about 16mT.

[0124] (2) Single coil fine 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, and the solving accuracy is higher. The dielectric properties of the superconducting tape insulation material are equivalent to air, so an air domain is added between the superconducting tapes to equivalent the insulated coil, as shown in Figure 6 .

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

[0127] (3) AC loss calculation

[0128] Figure 8 is a schematic diagram of the target coil current density and electric field distribution of the superconducting reactor at 0.015s. 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 period of the superconducting tape, as shown in Figure 9The calculation results are not stable in the first half cycle due to the zero initial condition. The AC loss power in the second half cycle is averaged to get the AC loss of a single coil winding, which is then multiplied by the number of coil windings in a single phase of the toroidal reactor M and by 3 (three phases) to get the total AC loss P of the superconducting shunt reactor.

[0129]

[0130] The foregoing description of the examples has been presented for the purposes of con- ciliation and enabling those of ordinary skill in the art to make and use the invention. Modifications, obvious to those of ordinary skill in the art, which are based on the general principles of the invention, can readily be made by those skilled in the art without departing from the scope of the invention. Accordingly, the invention is not limited to the examples described herein, but rather the scope of the invention is to be accorded the full scope consistent with the claims, and equivalents thereof.

Claims

1. A method for simulating AC losses in superconducting reactors based on in-situ substitution, characterized in that, Includes the following steps: S1: Using multiphysics finite element simulation software, for the reactor structure, the finite element method is used to replace the superconducting coils except the superconducting coil windings to be analyzed with regular geometric structures in situ. S2: Based on the simplified results in S1, construct a three-dimensional simplified model and a refined model of a single coil of the reactor structure. Solve for the inductance and magnetic field distribution parameters through the three-dimensional simplified model of the single coil. Set boundary conditions through the refined model and the obtained inductance and magnetic field distribution parameters. Solve for the electric field and current density inside the superconducting tape through Maxwell's equations. S3: Integrate the product of the electric field and current density inside the superconducting tape obtained in S2 to obtain the AC loss power, and handle the problem that the power has not reached a steady state under zero initial conditions in order to calculate the AC loss of the superconducting reactor coil winding. S2 specifically includes the following steps: S2-1: Construct a simplified three-dimensional model that treats the coil as an equivalent loop conductor without subdividing the number of turns, and use this model to solve for the coil inductance, overall magnetic field distribution and related parameters. S2-2: Construct a three-dimensional fine model, which depicts the shape of each turn and adds an air domain to be equivalent to an insulated coil, and sets the excitation of AC current to be applied to the single-phase coil winding of the reactor. S2-3: Based on the magnetic field calculated by the simplified model in S1, set the boundary conditions, and solve the electric field and current density distribution by performing transient field simulation according to Maxwell's equations; S3 specifically includes the following steps: S3-1: Enable the volume integration function in the simulation software. Based on the electric field and current density data in the superconducting tape obtained in S2, perform product integration according to the pre-set integration region 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 value of AC loss of a single coil winding under steady-state conditions; S3-4: Based on the number of coil windings in a single phase of a superconducting reactor and the characteristics of its three-phase structure, the total AC loss of the superconducting reactor coil windings is calculated, providing key quantitative indicators for the performance evaluation and optimized design of the superconducting reactor.

2. The method for simulating AC losses of superconducting reactors based on in-situ substitution according to claim 1, characterized in that, S1 specifically includes the following steps: S1-1: Based on multiphysics finite element simulation software and selecting the finite element method, the physical system of the superconducting reactor is decomposed into tiny mathematical units for solution; S1-2: Analyze the ring structure of the superconducting reactor, and identify the ring structure of the superconducting reactor as a ring-shaped combination of multiple superconducting insulated superconducting coils; S1-3: For superconducting coil windings, after selecting the winding to be analyzed, the remaining superconducting coils are replaced in situ.

3. The method for simulating AC losses of superconducting reactors based on in-situ substitution according to claim 1, characterized in that, S2-1 specifically includes the following steps: Based on the actual structure and electromagnetic characteristics of superconducting reactors, a single coil is abstracted and simplified to determine the specific geometric shape and size parameters of it as an equivalent ring conductor. A three-dimensional basic model framework is constructed without considering the subdivision of the number of turns. Based on the constructed simplified three-dimensional model framework, calculation conditions are set according to electromagnetic theory and the functional requirements of simulation software; The solver in the multiphysics finite element simulation software is used to calculate the model and obtain the relevant electromagnetic parameters of the coil. S2-2 specifically includes the following steps: Based on the actual number of turns, shape details, and relative positional relationships of each turn of a single coil in a superconducting reactor, a three-dimensional fine model framework capable of depicting the shape of each turn is constructed in simulation software. An air domain is added to the model corresponding to the region between superconducting tapes to represent the actual physical state of the insulated coil. Based on the working principle and simulation requirements of superconducting reactors, parameters for passing alternating current into the single-phase coil winding of the reactor are set. The parameters of the alternating current include the amplitude, frequency, and phase information of the current.

4. The method for simulating AC losses of superconducting reactors based on in-situ substitution according to claim 1, characterized in that, S2-3 specifically includes the following steps: Extract the magnetic field data obtained from the simplified model calculation in S1. The magnetic field data includes magnetic field strength, magnetic field direction, and magnetic field distribution information at different spatial locations. Organize and analyze the magnetic field data to determine its correspondence and range of action in the three-dimensional fine model. Based on the magnetic field data, 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 simplified model in S1. The three-dimensional fine model with predefined boundary conditions is substituted into the transient field simulation solution system based on Maxwell's equations. Taking into account the material properties, geometric structure, and applied AC current of the model, the electric field and current density distribution of the superconducting tape inside the model during the transient process are calculated iteratively using simulation software.

5. The method for simulating AC losses of superconducting reactors based on in-situ substitution according to claim 1, characterized in that, S3-1 specifically includes the following steps: In the multiphysics finite element simulation software, the volume integration function module is enabled to extract the electric field and current density data in the superconducting tape from the result data obtained by S2 and import them into the calculation framework of the volume integration function. Based on the actual physical structure and properties of the superconducting tape in the superconducting reactor, a precise integration region is set in the simulation software; The computational capabilities of finite element simulation software are used to perform point-by-point product calculations on electric field and current density data, and integration is performed within a set integration region. The integral value within one cycle is gradually accumulated according to the time step, thereby obtaining a preliminary value of the AC loss power of the superconducting tape within one cycle.

6. The method for simulating AC losses of superconducting reactors based on in-situ substitution according to claim 1, characterized in that, S3-2 specifically includes the following steps: Obtain the preliminary calculation results of the AC loss power of the superconducting tape obtained in S3-1 within one cycle, visualize the data sequence, and plot the power change curve over time. Based on the theoretical characteristics of the electromagnetic system under zero initial conditions, and by comparing the expected variation of AC power loss under normal steady-state conditions, we focus on the fluctuation of the data sequence in the initial stage, i.e., the first half of the cycle. By statistically analyzing the amplitude, frequency, and differences in subsequent stable data of the fluctuations, the specific manifestations of the instability characteristics are 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 are analyzed.

7. The method for simulating AC losses of superconducting reactors based on in-situ substitution according to claim 1, characterized in that, S3-3 specifically includes the following steps: From the AC loss power data sequence obtained from S3-2, the data portion within the second half-cycle is extracted. Using a mathematical averaging algorithm, the data of the second half-cycle is calculated to obtain the average AC loss power value within that cycle. This value is an approximation of the AC loss of a single coil winding under steady-state conditions.

8. The method for simulating AC losses of superconducting reactors based on in-situ substitution according to claim 1, characterized in that, S3-4 specifically includes the following steps: Obtain the accurate number of coil windings in a single phase of the superconducting reactor, and determine whether the single-phase results need to be expanded by the corresponding factor. The approximate AC loss of a single coil winding in 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 multiply the sum of the single-phase AC losses by the number of phases to calculate the total AC loss of the superconducting reactor coil winding.

Images