Structural optimization method of superconducting annular air-core reactor, medium and program product

Abstract

The invention relates to a superconductive annular air-core reactor structure optimization method, a medium and a program product, and the optimization method comprises the steps: optimizing the structure parameters of a superconductive reactor through an MATLAB and COMSOL joint simulation technology, and carrying out the optimization of the structure parameters of the superconductive reactor through a multi-objective genetic algorithm, thereby achieving the optimization of the structure parameters of the superconductive reactor. Iterative optimization is conducted on structural parameters such as the coil inner diameter, the surrounding radius, the number of turns of the coils, the number of the coils and the number of parallel branches of the electric reactor, the optimization target comprises the minimum strip use amount and alternating current loss, and in the optimal solution set, according to the strip use amount and the alternating current loss, the strip cost and the refrigeration cost are calculated. And finally, outputting an optimal structure parameter meeting a design index so as to realize the minimization of the total cost. Compared with the prior art, the method can be used for structural optimization of the superconducting reactors with different capacities, structural parameters with the lowest cost under different indexes can be obtained by setting constraint conditions, and economic benefits of reactor design are improved.

Description

Technical Field

[0001] The invention relates to the technical field of superconducting power application design, and in particular to a structure optimization method, medium and program product of a superconducting annular air-core reactor. Background Art

[0002] As electricity demand continues to rise, the scale and capacity of power systems continue to expand, resulting in more serious problems with reactive power compensation and overvoltage in long-distance high-voltage transmission. Shunt reactors play a vital role in this context, mitigating these problems by adjusting reactive power balance, thereby optimizing voltage distribution, reducing line losses, and improving the overall efficiency of the power grid.

[0003] In the existing power system, reactors are mainly divided into two types: air-core and iron-core. Iron-core reactors are characterized by a high-permeability iron core and a closed magnetic circuit, which helps to confine the magnetic field mainly inside the reactor. However, iron-core reactors have magnetic saturation problems, resulting in nonlinear inductance and high noise during operation. In contrast, air-core reactors are favored for their stable inductance values ​​and low noise characteristics. But as the complexity of power systems increases, the footprint and electromagnetic compatibility issues of reactors have become more prominent, especially in urban center areas where space is limited.

[0004] In order to solve these problems, the researchers proposed the design of a ring-shaped hollow reactor, which can effectively confine the magnetic field inside the reactor and reduce magnetic field leakage. In addition, the reactor made of superconducting materials works at liquid nitrogen temperature and exhibits zero resistance characteristics. It has the advantages of high current density, light weight, compact size and low noise, making it an ideal choice for urban power grids.

[0005] In view of the high cost of high-temperature superconducting tapes, it is particularly important to conduct an economic analysis of superconducting reactors. At the same time, considering that superconducting reactors need to work in low-temperature environments, the cost of cooling power has become a factor that cannot be ignored. Therefore, the cost optimization goal of the reactor is mainly focused on reducing the cost of tapes and cooling costs, while ensuring that the device parameters meet the requirements. Through this comprehensive consideration, researchers are in urgent need of designing a superconducting reactor that is both economical and efficient, and a structural optimization method for superconducting annular hollow reactors that meets the needs of modern power systems. Summary of the invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a structural optimization method, medium, and program product for a superconducting annular hollow reactor. The present invention can be used for structural optimization of superconducting reactors of different capacities. By setting constraints, the structural parameters with the lowest cost under different indicators can be obtained, thereby improving the economic benefits of the reactor design.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A first aspect of the present invention provides a method for optimizing the structure of a superconducting annular air-core reactor, comprising the following steps:

[0009] S1. Initialization: setting the initial structural parameters of the superconducting reactor, including the inner diameter of the coil, the winding radius, the number of coil turns, the number of coils, and the number of parallel branches;

[0010] S2. Inductance adjustment: adjust the number of turns of the coil, perform rough adjustment using the Newman formula of MATLAB, and perform fine adjustment based on the magnetic energy method of COMSOL simulation, so that the inductance value reaches the design index;

[0011] S3, critical current calculation: calculate the critical current after adjusting the number of turns, and determine whether the critical current, inductance and geometry meet the constraints. If not, reinitialize the variables; if yes, continue to the next step;

[0012] S4. Calculation of strip material usage and AC loss: Calculate the strip material usage after adjusting the number of turns through MATLAB; Calculate the AC loss through COMSOL simulation;

[0013] S5, optimization iteration: use a multi-objective genetic algorithm to iteratively optimize the structural parameters until the optimal solution set with the least amount of strip material and the lowest AC loss is found;

[0014] S6. Cost calculation: In the optimal solution set, according to the amount of strip and AC loss, the strip cost and the cooling cost required to meet the AC loss are calculated, and the total cost is obtained by combining the cost of other components of the superconducting reactor, and the solution with the lowest total cost in the optimal solution set is found;

[0015] S7. Output results: Output the optimal solution, including the coil inner diameter, winding radius, number of coil turns, number of coils, number of parallel branches, and the corresponding critical current, inductance value, strip usage, AC loss, and total cost.

[0016] Furthermore, S2 specifically includes the following steps:

[0017] S2-1. First, the number of coil turns is roughly adjusted by applying the Newman formula through MATLAB software to quickly obtain an inductance value close to the design requirements;

[0018] S2-2. Use the magnetic energy method of COMSOL software to make detailed adjustments to the inductance, and use finite element analysis to accurately calculate the electromagnetic field distribution to ensure that the inductance value accurately meets the design specifications.

[0019] Furthermore, S3 specifically includes the following steps:

[0020] S3-1. Calculate the critical current after adjusting the number of turns;

[0021] S3-2, determine whether the calculated critical current meets the inductance and geometric constraints. If the calculated critical current does not meet the constraints, re-initialize the variables in S1 and repeat steps S1 to S3 until the structural parameters that meet the conditions are found.

[0022] Furthermore, in S3, the process of determining whether the calculated critical current satisfies the inductance and geometric constraints includes: verifying whether the critical current value is within the safe operating range of the superconducting material, and whether it meets the geometric design requirements of the reactor, wherein the geometric design requirements include the design requirements of the size, shape, and arrangement of the coil.

[0023] Furthermore, S5 specifically includes the following steps:

[0024] Initialize the population: randomly generate a group of individuals, each of which represents a potential solution, including the inner diameter of the coil, the winding radius, the number of coil turns, the number of coils, and the number of parallel branches;

[0025] Calculate fitness: Use a multi-objective function to evaluate the fitness value of each individual and obtain a fitness vector;

[0026] Pareto front sorting: Sort individuals according to their fitness vectors, divide them into different Pareto fronts, and identify the set of non-inferior solutions;

[0027] Calculate the crowding distance: In each Pareto front, calculate the distance between each individual and its neighboring individuals to maintain the diversity of the population;

[0028] Selection operation: select a group of individuals from the population to generate the next generation of individuals. The selection strategy is usually based on the Pareto frontier and crowding distance;

[0029] Crossover and mutation operations: Perform crossover and mutation operations on the selected individuals to generate new individuals and add them to the next generation population;

[0030] Update the population: replace the original individuals with new ones to form the next generation of population;

[0031] Iterate until convergence: Repeat the above steps until the number of iterations is met or a satisfactory solution set is found, which is used as the optimal solution set with the lowest total cost and lowest AC loss.

[0032] Furthermore, in the superconducting annular air-core reactor, each coil is a double-pancake coil, which is wound around a circle and connected in series and parallel with each other through metal parts, and finally divided into multiple parallel branches;

[0033] In S5, the structural parameters of the reactor are optimized by using the genetic algorithm toolbox in MATLAB. The optimization algorithm is a multi-objective genetic algorithm, and the optimization goal is to minimize the amount of strip material and the AC loss.

[0034] In S2 to S4, the inductance and AC loss of the reactor are calculated using an equivalent simplified model in COMSOL.

[0035] Furthermore, in S6, the cost calculation specifically includes the following steps:

[0036] Strip cost calculation: Calculate the strip cost based on the strip usage and the current market strip price

[0037] Refrigeration cost calculation: Determine the cooling capacity of the refrigeration system based on AC losses, and calculate the purchase price, operating costs, refrigerant costs and possible maintenance costs of the refrigeration system.

[0038] Total cost calculation: Add the calculated strip cost and refrigeration cost together, and combine them with the cost of other components of the superconducting reactor to get the total cost of the reactor.

[0039] Furthermore, in the calculation of the cooling cost, the net cooling capacity of the refrigeration system must be greater than the AC loss and the system heat leakage. The net cooling capacity of the refrigeration system is related to the cooling temperature. The lower the cooling temperature, the smaller the net cooling capacity. Take Figure 4 as an example.

[0040] A second aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-mentioned method for optimizing the structure of the superconducting annular air-core reactor.

[0041] A third aspect of the present invention provides a computer program product, comprising a computer program, which implements the above-mentioned method for optimizing the structure of the superconducting annular air-core reactor when executed by a processor.

[0042] Compared with the prior art, the present invention has the following technical advantages:

[0043] The present invention optimizes the structural parameters of the superconducting annular hollow reactor by adopting a multi-objective genetic algorithm, thereby achieving significant economic benefits and performance improvements. First, the electromagnetic performance and cost-effectiveness of the reactor are comprehensively evaluated through the MATLAB and COMSOL joint simulation platform to ensure the accuracy and reliability of the design. Secondly, the optimization process takes into account the AC loss of the superconducting material, ensuring the efficient operation of the reactor in the superconducting state and reducing the operating cost. In addition, the present invention also comprehensively considers the refrigeration cost, and through an accurate cost calculation model, it achieves effective control of the total cost of the reactor and improves the economy. Finally, through iterative optimization, the optimal structural parameters with the least amount of strip and the lowest AC loss under the premise of meeting the design indicators are found, thereby achieving the performance optimization and cost minimization of the superconducting annular hollow reactor. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic diagram of the basic structure of a superconducting toroidal reactor;

[0045] Figure 2 This is an optimization flow chart of an embodiment of the present invention;

[0046] Figure 3 This is an optimization result diagram of an embodiment of the present invention, where each point is a set of solutions;

[0047] Figure 4 This is a schematic diagram showing an example of the relationship between the net cooling capacity and the cooling temperature of a refrigeration system. DETAILED DESCRIPTION

[0048] The purpose of the present invention is to propose a structural optimization method for a superconducting annular hollow reactor, and to calculate the structural parameters of the superconducting reactor through joint simulation of MATLAB and COMSOL, so as to achieve the lowest total cost and improve the economic benefit. The present invention optimizes the structural parameters of the superconducting reactor through joint simulation of MATLAB and COMSOL, so as to achieve the lowest total cost and improve the economic benefit. The optimization variables are the structural parameters of the reactor, including the inner diameter of the coil, the annular radius, the number of coils, the number of coil turns and the number of parallel branches; the optimization objectives are to minimize the amount of strip material, minimize the AC loss and minimize the total cost; the optimization algorithm adopts a multi-objective genetic algorithm. The present invention can be used for the structural optimization of superconducting reactors of different capacities. By setting constraints, the structural parameters with the lowest cost under different indicators can be obtained, thereby improving the economic benefit of the reactor design.

[0049] The superconducting annular air-core reactor is divided into three phases. Each single-phase reactor is composed of multiple circular double-pancake coils, which are evenly arranged in a ring around the central axis with a certain radius, such as Figure 1 Among them, R is the winding radius, r is the inner radius of a single coil, nt is the number of turns, nc is the number of coils, and D is the diameter of the entire reactor.

[0050] The working principle of the superconducting reactor is: when the load in the line is small or the end is open, the power frequency overvoltage phenomenon will occur due to the capacitance effect of the long line. Since the inductor and the capacitor have the characteristics of phase reversal, the input of the reactor will compensate for the capacitive effect of the line, limit the increase of the power frequency voltage in the system, and realize the local consumption of reactive power. By selecting a suitable inductor to make the inductor and the capacitor resonate in parallel, the capacitance effect is completely eliminated.

[0051] 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.

[0052] Example 1

[0053] The structural optimization method of the superconducting annular air-core reactor in this embodiment includes the following steps:

[0054] S1. Initialization: setting the initial structural parameters of the superconducting reactor, including the inner diameter of the coil, the winding radius, the number of coil turns, the number of coils, and the number of parallel branches;

[0055] S2. Inductance adjustment: adjust the number of turns of the coil, perform rough adjustment by Newman formula of MATLAB, and perform fine adjustment by magnetic energy method of COMSOL, so that the inductance value reaches the design index;

[0056] The specific steps include:

[0057] S2-1. First, the number of coil turns is roughly adjusted by applying the Newman formula through MATLAB software to quickly obtain an inductance value close to the design requirements;

[0058] S2-2. Use the magnetic energy method of COMSOL software to make detailed adjustments to the inductance, and use finite element analysis to accurately calculate the electromagnetic field distribution to ensure that the inductance value accurately meets the design specifications.

[0059] S3, critical current calculation: calculate the critical current after adjusting the number of turns, and determine whether the critical current, inductance and geometry meet the constraints. If not, reinitialize the variables; if yes, continue to the next step;

[0060] The specific steps include:

[0061] S3-1. Calculate the critical current after adjusting the number of turns;

[0062] S3-2, determine whether the calculated critical current meets the inductance and geometric constraints. If the calculated critical current does not meet the constraints, re-initialize the variables in S1 and repeat steps S1 to S3 until the structural parameters that meet the conditions are found.

[0063] Furthermore, in S3, the process of determining whether the calculated critical current satisfies the inductance and geometric constraints includes: verifying whether the critical current value is within the safe operating range of the superconducting material, and whether it meets the geometric design requirements of the reactor, wherein the geometric design requirements include the design requirements of the size, shape, and arrangement of the coil.

[0064] S4. Calculation of strip material usage and AC loss: Calculate the strip material usage after adjusting the number of turns through MATLAB; Calculate the AC loss through COMSOL simulation;

[0065] S5, optimization iteration: use a multi-objective genetic algorithm to iteratively optimize the structural parameters until the optimal solution set with the least amount of strip material and the lowest AC loss is found;

[0066] The specific steps include:

[0067] Initialize the population: randomly generate a group of individuals, each of which represents a potential solution, including the inner diameter of the coil, the winding radius, the number of coil turns, the number of coils, and the number of parallel branches;

[0068] Calculate fitness: Use a multi-objective function to evaluate the fitness value of each individual and obtain a fitness vector;

[0069] Pareto front sorting: Sort individuals according to their fitness vectors, divide them into different Pareto fronts, and identify the set of non-inferior solutions;

[0070] Calculate the crowding distance: In each Pareto front, calculate the distance between each individual and its neighboring individuals to maintain the diversity of the population;

[0071] Selection operation: select a group of individuals from the population to generate the next generation of individuals. The selection strategy is usually based on the Pareto frontier and crowding distance;

[0072] Crossover and mutation operations: Perform crossover and mutation operations on the selected individuals to generate new individuals and add them to the next generation population;

[0073] Update the population: replace the original individuals with new ones to form the next generation of population;

[0074] Iterate until convergence: Repeat the above steps until the number of iterations is met or a satisfactory solution set is found, which is used as the optimal solution set with the lowest total cost and lowest AC loss.

[0075] In S2 to S4, the inductance and AC loss of the reactor are calculated using an equivalent simplified model in COMSOL.

[0076] In S5, the structural parameters of the reactor are optimized by using the genetic algorithm toolbox in MATLAB. The optimization algorithm is a multi-objective genetic algorithm, and the optimization goal is to minimize the amount of strip material and the AC loss.

[0077] S6. Cost calculation: In the optimal solution set, according to the amount of strip and AC loss, the strip cost and the cooling cost required to meet the AC loss are calculated, and the total cost is obtained by combining the cost of other components of the superconducting reactor, and the solution with the lowest total cost in the optimal solution set is found;

[0078] S7. Output results: Output the optimal solution, including the coil inner diameter, winding radius, number of coil turns, number of coils, number of parallel branches, and the corresponding critical current, inductance value, strip usage, AC loss, and total cost.

[0079] In the superconducting annular air-core reactor, each coil is a double-pancake coil, which is wound around a circle and connected in series and parallel with each other through metal parts, and finally divided into multiple parallel branches.

[0080] The working principle of the present invention is based on a multi-objective genetic algorithm, which optimizes the structural parameters of the superconducting annular air-core reactor by simulating natural selection and genetic mechanisms. The algorithm initializes a population containing multiple potential solutions, each of which represents a set of structural parameters of the reactor. These parameters include the inner diameter of the coil, the winding radius, the number of coil turns, the number of coils, and the number of parallel branches, which together determine the performance of the reactor, such as the amount of strip material used and the AC loss.

[0081] In the iterative process, the algorithm evaluates the fitness of each individual, that is, their performance in the multi-objective function, which aims to minimize the amount of strip and AC loss. Through selection, crossover and mutation operations, the population continues to evolve and gradually approaches the Pareto optimal front. The Pareto optimal front consists of a set of non-inferior solutions that provide the best trade-off between multiple objectives.

[0082] Finally, the algorithm converges to an optimal solution set, which represents the reactor structural parameters that can achieve the lowest cost while satisfying the design constraints. These parameters not only take into account the physical properties of superconducting materials, but also the refrigeration cost and manufacturing cost, ensuring the economy and efficiency of the reactor in practical applications. Through the method of the present invention, designers can quickly find the reactor design that best suits the needs of a specific application, thereby improving the performance of superconducting reactors and reducing costs.

[0083] During specific implementation, the present invention is described by taking the following process as an example:

[0084] Figure 2This is a schematic diagram of the entire optimization process. The optimization variables are the structural parameters of the 10kV / 1MVar reactor. The optimization goal is to minimize the amount of strip material and the AC loss. The optimization method uses a multi-objective genetic algorithm. The specific process is as follows:

[0085] 1. First, initialize the variables, including the inner diameter of the coil, the winding radius, the number of coil turns, the number of coils, and the number of parallel branches.

[0086] 2. Adjust the number of turns of the reactor coil so that the inductance reaches 0.318H and reaches the design index of 1Mvar. This is divided into coarse adjustment and fine adjustment. Coarse adjustment is to calculate the inductance through the Newman formula of MATLAB, and fine adjustment is to calculate the inductance through the magnetic energy method of COMSOL.

[0087] 3. After the number of turns is adjusted, the critical current is calculated to determine whether the critical current, inductance and geometry meet the constraints. If not, the variables are reinitialized; if not, continue to the next step.

[0088] 4. Calculate the strip usage and AC loss of the reactor through the equivalent COMSOL model. When the population algebra reaches the set value, output the optimal solution set.

[0089] Figure 3 The coordinate axes are two optimization targets, each of which is a feasible solution. The red dots represent the optimal solution set. Based on engineering experience, the economic analysis of the optimal solution set is carried out, the strip cost and the refrigeration cost are calculated, and the structural parameters of the superconducting reactor with the lowest cost are shown in Table 1.

[0090] Table 1 Structural parameters of the lowest cost 10kV / 1MVar superconducting annular air-core reactor

[0091]

[0092] Example 2

[0093] This embodiment provides a computer-readable storage medium, on which a specific computer program is stored. When the program is executed by a processor, each step of the structure optimization method of the superconducting annular air-core reactor described above can be implemented. This storage medium can be any form of computer-readable medium, such as a hard disk, CD-ROM, DVD, flash drive, ROM, RAM, etc., or a digital signal transmitted through a computer network.

[0094] The computer program contains a series of instructions designed to guide the processor to complete the optimization process of the structural parameters of the superconducting reactor. The program will first initialize the initial structural parameters of the reactor, then adjust the inductance through the simulation software, then calculate the critical current, and determine whether the inductance and geometric constraints are met. If the conditions are met, the program will continue to calculate the cost, including the amount of tape, AC loss and cooling cost. After that, the program will use a multi-objective genetic algorithm to perform optimization iterations until the optimal solution set with the lowest cost is found. Finally, the program will output the optimal solution set including parameters such as the inner diameter of the coil, the winding radius, the number of coil turns, and the corresponding critical current, inductance value, tape amount, AC loss and total cost. The provision of this storage medium enables any user with the corresponding hardware equipment to realize the structural optimization of the superconducting ring air reactor by running the program, greatly improving the design efficiency and economic benefits, while also reducing the dependence on professional designers.

[0095] Example 3

[0096] This embodiment provides a computer program product, the core of which is a specific computer program. The computer program is designed to execute a structural optimization method for superconducting annular air-core reactors. When the program runs on a processor of a computer system, it can automatically execute a series of predetermined optimization steps, including initializing the structural parameters of the reactor, adjusting the number of coil turns to meet specific inductance design indicators, calculating the critical current and verifying whether it meets the inductance and geometric constraints, calculating the amount of strip material and AC loss, and calculating the total cost by comprehensively considering the refrigeration cost. Through a multi-objective genetic algorithm, the program can iteratively search for and determine the optimal solution set, which will achieve the goal of minimizing the amount of strip material and minimizing the AC loss, while ensuring the lowest total cost. This computer program product not only improves design efficiency, but also provides an innovative solution for the design and manufacture of superconducting reactors through precise calculation and optimization.

[0097] 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 optimizing the structure of a superconducting annular air-core reactor, characterized in that: The following steps are involved: S1. Initialization: setting the initial structural parameters of the superconducting reactor, including the inner diameter of the coil, the winding radius, the number of coil turns, the number of coils, and the number of parallel branches; S2. Inductance adjustment: adjust the number of turns of the coil, perform rough adjustment by Newman formula of MATLAB, and perform fine adjustment by magnetic energy method of COMSOL, so that the inductance value reaches the design index; S3, critical current calculation: calculate the critical current after adjusting the number of turns, and determine whether the critical current, inductance and geometry meet the constraints. If not, reinitialize the variables; if yes, continue to the next step; S4. Calculation of strip material usage and AC loss: Calculate the strip material usage after adjusting the number of turns through MATLAB; Calculate the AC loss through COMSOL simulation; S5, optimization iteration: use a multi-objective genetic algorithm to iteratively optimize the structural parameters until the optimal solution set with the least amount of strip material and the lowest AC loss is found; S6. Cost calculation: In the optimal solution set, according to the amount of strip and AC loss, the strip cost and the cooling cost required to meet the AC loss are calculated, and the total cost is obtained by combining the cost of other components of the superconducting reactor, and the solution with the lowest total cost in the optimal solution set is found; S7. Output results: Output the optimal solution, including the coil inner diameter, winding radius, number of coil turns, number of coils, number of parallel branches, and the corresponding critical current, inductance value, strip usage, AC loss, and total cost.

2. The structural optimization method of a superconducting annular air-core reactor according to claim 1, characterized in that: S2 specifically includes the following steps: S2-1. First, the Newman formula is used to roughly adjust the number of coil turns through MATLAB software to quickly obtain an inductance value close to the design requirements; S2-2. Use the magnetic energy method of COMSOL software to make detailed adjustments to the inductance, and use finite element analysis to accurately calculate the electromagnetic field distribution to ensure that the inductance value accurately meets the design specifications.

3. The structural optimization method of a superconducting annular air-core reactor according to claim 1, characterized in that: S3 specifically includes the following steps: S3-1. Calculate the critical current after adjusting the number of turns; S3-2, determine whether the calculated critical current meets the inductance and geometric constraints. If the calculated critical current does not meet the constraints, re-initialize the variables in S1 and repeat steps S1 to S3 until the structural parameters that meet the conditions are found.

4. The structural optimization method of a superconducting annular air-core reactor according to claim 3, characterized in that: In S3, the process of judging whether the calculated critical current satisfies the inductance and geometric constraints includes: verifying whether the critical current value is within the safe operating range of the superconducting material, and whether it meets the geometric design requirements of the reactor, wherein the geometric design requirements include the design requirements of the size, shape, and arrangement of the coil.

5. The structural optimization method of a superconducting annular air-core reactor according to claim 1, characterized in that: S5 specifically includes the following steps: Initialize the population: randomly generate a group of individuals, each of which represents a potential solution, including the inner diameter of the coil, the winding radius, the number of coil turns, the number of coils, and the number of parallel branches; Calculate fitness: Use a multi-objective function to evaluate the fitness value of each individual and obtain a fitness vector; Pareto front sorting: Sort individuals according to their fitness vectors, divide them into different Pareto fronts, and identify the set of non-inferior solutions; Calculate the crowding distance: In each Pareto front, calculate the distance between each individual and its neighboring individuals to maintain the diversity of the population; Selection operation: select a group of individuals from the population to generate the next generation of individuals. The selection strategy is usually based on the Pareto frontier and crowding distance; Crossover and mutation operations: Perform crossover and mutation operations on the selected individuals to generate new individuals and add them to the next generation population; Update the population: replace the original individuals with new ones to form the next generation of population; Iterate until convergence: Repeat the above steps until the number of iterations is met or a satisfactory solution set is found, which is used as the optimal solution set with the lowest total cost and lowest AC loss.

6. The method for optimizing the structure of a superconducting annular air-core reactor according to claim 1, characterized in that: In the superconducting annular air-core reactor, each coil is a double-pancake coil, which is wound around a circle and connected in series and parallel with each other through metal parts, and finally divided into multiple parallel branches.

7. The method for optimizing the structure of a superconducting annular air-core reactor according to claim 1, characterized in that: In S5, the structural parameters of the reactor are optimized by the genetic algorithm toolbox in MATLAB. The optimization algorithm is a multi-objective genetic algorithm, and the optimization goal is to minimize the amount of strip material and the lowest AC loss.

8. The method for optimizing the structure of a superconducting annular air-core reactor according to claim 1, characterized in that: In S2 to S4, the inductance and AC loss of the reactor are calculated using an equivalent simplified model in COMSOL.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for structural optimization of a superconducting annular air-core reactor described in any one of claims 1 to 8 are implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the method for optimizing the structure of the superconducting annular air-core reactor described in any one of claims 1 to 8 is implemented.

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