A structural optimization method, medium, and program product for a superconducting annular hollow reactor

Abstract

The present invention relates to a structural optimization method, medium, and program product for a superconducting annular hollow reactor. The optimization method optimizes the structural parameters of the superconducting reactor using MATLAB and COMSOL joint simulation technology. A multi-objective genetic algorithm is used to iteratively optimize structural parameters such as the reactor's coil inner diameter, winding radius, number of coil turns, number of coils, and number of parallel branches. The optimization objectives include minimizing strip material usage and AC loss. Within the optimal solution set, strip material cost and cooling cost are calculated based on the strip material usage and AC loss. Ultimately, the optimal structural parameters that meet design specifications are output to minimize total cost. Compared with existing technologies, 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 specifications can be obtained, thereby improving the economic benefits of reactor design.

Description

Technical Field

[0001] The present 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 hollow reactor. Background Art

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

[0003] In existing power systems, reactors are primarily classified into two types: air-core and iron-core. Iron-core reactors are characterized by a high-permeability core and a closed magnetic circuit, which helps confine the magnetic field primarily within the reactor. However, iron-core reactors suffer from magnetic saturation, resulting in nonlinear inductance and loud operating noise. In contrast, air-core reactors are favored for their stable inductance and low noise characteristics. However, as power systems increase in complexity, reactor footprint and electromagnetic compatibility issues become more prominent, especially in space-constrained urban centers.

[0004] To address these issues, researchers have proposed a toroidal hollow-core reactor design. This structure effectively confines the magnetic field within the reactor, reducing magnetic field leakage. Furthermore, reactors made of superconducting materials exhibit zero resistance when operated at liquid nitrogen temperatures. These reactors offer advantages such as high current density, light weight, compact size, and low noise, making them ideal for use in urban power grids.

[0005] Given the high cost of high-temperature superconducting tape, economic analysis of superconducting reactors is particularly important. Furthermore, given that superconducting reactors must operate in cryogenic environments, cooling power costs are a significant factor. Therefore, reactor cost optimization primarily focuses on reducing tape and cooling costs while ensuring that device parameters meet requirements. This comprehensive consideration necessitates the design of cost-effective and efficient superconducting reactors to meet the demands of modern power systems. Researchers are urgently seeking structural optimization methods for superconducting annular hollow reactors. Summary of the Invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and 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: Set 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 in MATLAB, and perform fine adjustment based on the magnetic energy method simulated by COMSOL, so that the inductance value meets 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 so, proceed 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 using MATLAB; calculate the AC loss using 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, calculate the strip cost and the cooling cost required to meet the AC loss based on the strip usage and AC loss. Combined with the costs of other components of the superconducting reactor, the total cost is obtained 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 material usage, AC loss, and total cost.

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

[0017] S2-1. First, use the Newman formula in MATLAB to roughly adjust the number of coil turns to quickly obtain an inductance value close to the design requirements.

[0018] S2-2. Use the magnetic energy method of COMSOL software to carefully adjust the inductance, and accurately calculate the electromagnetic field distribution through finite element analysis 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, reinitialize 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 coil inner diameter, winding radius, number of coil turns, number of coils, and 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 non-inferior solution sets;

[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 produce the next generation of individuals. The selection strategy is usually based on the Pareto front 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 hollow 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 reactor structural parameters are optimized 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] Calculation of cooling costs: Based on AC losses, determine the cooling capacity of the cooling system and calculate the purchase price, operating costs, refrigerant costs, and possible maintenance costs of the cooling system.

[0038] Total cost calculation: Add the calculated strip cost and refrigeration cost, and combine them with the costs of other components of the superconducting reactor to obtain 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 a 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 using a multi-objective genetic algorithm, achieving significant economic benefits and performance improvements. First, a comprehensive evaluation of the electromagnetic performance and cost-effectiveness of the reactor is performed 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 operating costs. 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 economic efficiency. Finally, through iterative optimization, the optimal structural parameters with the least amount of strip material 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 This is a schematic diagram of the basic structure of a superconducting ring reactor;

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

[0046] Figure 3 This is the optimization result diagram of the 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 of a refrigeration system and the refrigeration temperature. DETAILED DESCRIPTION

[0048] The purpose of the present invention is to propose a structural optimization method for a superconducting annular hollow reactor. By using MATLAB and COMSOL joint simulation, the structural parameters of the superconducting reactor are calculated to achieve the lowest total cost and improve economic benefits. The present invention optimizes the structural parameters of the superconducting reactor through MATLAB and COMSOL joint simulation to achieve the lowest total cost and improve economic benefits. 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 used, 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 benefits of the reactor design.

[0049] The superconducting annular hollow 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 Where 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 operating principle of a superconducting reactor is that when the load on a line is light or the end is open, the capacitive effect of a long line can cause power-frequency overvoltage. Because inductance and capacitance are in anti-phase, the use of a reactor compensates for the capacitive effect of the line, limiting the rise in power-frequency voltage in the system and achieving local reactive power absorption. By selecting the appropriate inductor to achieve parallel resonance between the inductor and capacitor, the capacitive effect is completely eliminated.

[0051] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. Component models, material names, connection structures, control methods, algorithms, and other features not explicitly described in this technical solution are considered 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: Set 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 using the Newman formula in MATLAB, and perform fine adjustment using the magnetic energy method in COMSOL, so that the inductance value reaches the design index;

[0056] The specific steps include:

[0057] S2-1. First, use the Newman formula in MATLAB to roughly adjust the number of coil turns to quickly obtain an inductance value close to the design requirements.

[0058] S2-2. Use the magnetic energy method of COMSOL software to carefully adjust the inductance, and accurately calculate the electromagnetic field distribution through finite element analysis 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 so, proceed 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, reinitialize 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 using MATLAB; calculate the AC loss using 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 coil inner diameter, winding radius, number of coil turns, number of coils, and 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 non-inferior solution sets;

[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 produce the next generation of individuals. The selection strategy is usually based on the Pareto front 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 reactor structural parameters are optimized 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, calculate the strip cost and the cooling cost required to meet the AC loss based on the strip usage and AC loss. Combined with the costs of other components of the superconducting reactor, the total cost is obtained 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 material usage, AC loss, and total cost.

[0079] In the superconducting annular hollow 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 is finally divided into multiple parallel branches.

[0080] The present invention utilizes a multi-objective genetic algorithm to optimize the structural parameters of superconducting toroidal air-core reactors by simulating natural selection and genetic mechanisms. The algorithm initializes a population of potential solutions, each representing a set of reactor structural parameters. These parameters include the coil inner diameter, winding radius, number of turns, number of coils, and number of parallel branches, which together determine reactor performance, such as coil material usage and AC losses.

[0081] During the iteration process, the algorithm evaluates the fitness of each individual—its performance against a multi-objective function designed to minimize strip usage and AC loss. Through selection, crossover, and mutation, the population evolves, gradually approaching the Pareto optimal front. The Pareto optimal front consists of a set of non-inferior solutions that offer the best trade-offs between multiple objectives.

[0082] Ultimately, the algorithm converges to an optimal solution set, representing the reactor structural parameters that achieve the lowest cost while satisfying the design constraints. These parameters take into account not only the physical properties of the superconducting material but also cooling and manufacturing costs, ensuring the reactor's economical and efficient performance in practical applications. This method enables designers to quickly identify the reactor design that best suits specific application requirements, thereby improving superconducting reactor performance and reducing costs.

[0083] During specific implementation, the present invention is described using 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 objectives are 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 coil inner diameter, winding radius, number of coil turns, number of coils, and number of parallel branches.

[0086] 2. Adjust the number of turns of the reactor coil to achieve an inductance of 0.318H, meeting the design target of 1 Mvar. This involves both coarse and fine adjustments. Coarse adjustments use the Newman equation in MATLAB to calculate the inductance, while fine adjustments use the magnetic energy method in COMSOL to calculate the inductance.

[0087] 3. After adjusting the number of turns, calculate the critical current and determine whether the critical current, inductance, and geometry meet the constraints. If not, reinitialize the variables. If not, continue to the next step.

[0088] 4. Calculate the strip material 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 represent the two optimization objectives, each of which represents a feasible solution. The red dots represent the optimal solution set. Based on engineering experience, an economic analysis of the optimal solution set was performed, calculating the strip material cost and cooling cost. 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 storing a specific computer program. When executed by a processor, the program implements the steps of the above-described method for optimizing the structure of a superconducting annular air-core reactor. The storage medium can be any form of computer-readable medium, such as a hard disk, CD-ROM, DVD, flash drive, ROM, RAM, or the like, or a digital signal transmitted via a computer network.

[0094] This computer program contains a series of instructions designed to guide a processor through the process of optimizing the structural parameters of a superconducting reactor. The program first initializes the initial structural parameters of the reactor, then adjusts the inductance using simulation software. It then calculates the critical current and determines whether the inductance and geometric constraints are met. If so, the program proceeds to cost calculations, including the amount of tape used, AC losses, and cooling costs. Next, the program applies a multi-objective genetic algorithm to iterate the optimization until the optimal solution with the lowest cost is found. Ultimately, the program outputs the optimal solution for parameters such as the coil inner diameter, winding radius, and number of turns, along with the corresponding critical current, inductance, tape used, AC losses, and total cost. The provision of this storage medium enables anyone with the appropriate hardware to run the program to optimize the structure of superconducting toroidal air-core reactors, significantly improving design efficiency and economic benefits while reducing reliance 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 a superconducting annular hollow reactor. 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 used and AC loss, and calculating the total cost by comprehensively considering the cooling cost. Through a multi-objective genetic algorithm, the program can iteratively search for and determine the optimal solution set, which will achieve the goals of minimizing the amount of strip material used 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 intended to facilitate understanding and use of the invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to these embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above-described embodiments. 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 hollow reactor, characterized in that: The following steps are involved: S1. Initialization: Set 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 using the Newman formula in MATLAB, and perform fine adjustment using the magnetic energy method in 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 so, proceed to the next step. S4. Calculation of strip material usage and AC loss: Calculate the strip material usage after adjusting the number of turns using MATLAB; calculate the AC loss using 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, calculate the strip cost and the cooling cost required to meet the AC loss based on the strip usage and AC loss. Combined with the costs of other components of the superconducting reactor, the total cost is obtained 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 material usage, AC loss, and total cost.

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

3. The structural optimization method of a superconducting annular hollow reactor according to claim 1, characterized in that: In S3, the following steps are specifically included: 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, reinitialize the variables in S1 and repeat steps S1 to S3 until the structural parameters that meet the conditions are found.

4. The method for optimizing the structure of a superconducting annular hollow reactor according to claim 3, characterized in that: 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.

5. The method for optimizing the structure of a superconducting annular hollow 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 coil inner diameter, winding radius, number of coil turns, number of coils, and 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 non-inferior solution sets; 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 based on the Pareto front 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 hollow reactor according to claim 1, characterized in that: In the superconducting annular hollow 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 is 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 through 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 according to 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 according to any one of claims 1 to 8 is implemented.

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