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

Abstract

The present invention relates to a structural optimization method for a superconducting annular air core reactor, a medium, and a program product. In the optimization method, structural parameters of a superconducting reactor are optimized by means of MATLAB and COMSOL joint simulation technology. By means of a multi-objective genetic algorithm, structural parameters of the reactor, such as the inner diameter of a coil, a winding radius, the number of coil turns, the number of coils, and the number of parallel branches, are iteratively optimized. Optimization objectives comprise minimizing the amount of strip material used and alternating current loss. In an optimal solution set, strip material costs and refrigeration costs are calculated on the basis of the amount of strip material used and the alternating current loss, and optimal structural parameters that meet design criteria are finally outputted, so as to minimize the total costs. Compared with the existing technology, the present invention can be used for structural optimization of superconducting reactors having different capacities. By setting constraint conditions, structural parameters with the lowest cost under different criteria can be obtained, thereby improving the economic benefits of reactor design.

Description

A method, dielectric, and program product for structural optimization of a superconducting toroidal hollow reactor. Technical Field

[0001] This invention relates to the field of superconducting power application design technology, and in particular to a structural optimization method, dielectric, and program product for a superconducting toroidal hollow reactor. Background Technology

[0002] With the continuous rise in electricity demand and the ongoing expansion of power system size and capacity, reactive power compensation and overvoltage issues in long-distance high-voltage transmission have become more severe. In this context, shunt reactors play a crucial role, 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 existing power systems, reactors are mainly classified 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 primarily within the reactor. However, iron-core reactors suffer from magnetic saturation, leading to inductance nonlinearity and relatively high operating noise. In contrast, air-core reactors are favored for their stable inductance and low-noise characteristics. However, with the increasing complexity of power systems, the footprint and electromagnetic compatibility issues of reactors have become more prominent, especially in space-constrained urban centers.

[0004] To address these issues, researchers proposed a toroidal hollow reactor design. This structure effectively confines the magnetic field within the reactor, reducing magnetic field leakage. Furthermore, reactors fabricated using superconducting materials operate at liquid nitrogen temperatures, exhibiting zero resistance. They also offer advantages such as high current density, light weight, compact size, and low noise, making them an ideal choice for urban power grids.

[0005] Given the high cost of high-temperature superconducting tapes, economic analysis of superconducting reactors is particularly important. Simultaneously, considering the need for superconducting reactors to operate in cryogenic environments, cooling power costs also become a significant factor. Therefore, the cost optimization objective of reactors primarily focuses on reducing tape and cooling costs while ensuring that device parameters meet requirements. Through this comprehensive consideration, researchers urgently need to design economical and efficient superconducting reactors to meet the needs of modern power systems, specifically a structural optimization method for superconducting toroidal hollow reactors. Invention Overview Technical solutions

[0006] The purpose of this invention is to overcome the defects of the prior art by providing a method, medium, and program product for optimizing the structure of a superconducting toroidal hollow reactor. This 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 efficiency of reactor design.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] The first aspect of this invention provides a method for structural optimization of a superconducting toroidal hollow reactor, comprising the following steps:

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

[0010] S2. Inductance Adjustment: Adjust the number of turns of the coil, perform coarse adjustment using the Newman formula in MATLAB, and fine adjustment using the magnetic energy method based on COMSOL simulation, so that the inductance value reaches the design specifications.

[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 they meet, 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 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 minimum strip material usage and the lowest AC loss is found.

[0014] S6. Cost Calculation: In the optimal solution set, calculate the cost of the strip and the cooling cost required to meet the AC loss based on the amount of strip material and AC loss. Combine the costs of other components of the superconducting reactor to obtain the total cost and find the solution with the lowest total cost in the optimal solution set.

[0015] S7. Output Results: Output the optimal solution, including coil inner diameter, winding radius, number of coil turns, number of coils, number of parallel branches, and the corresponding critical current, inductance value, tape 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 using the Newman formula in MATLAB software to quickly obtain an inductance value close to the design requirements.

[0018] S2-2. The inductor is finely adjusted using the magnetic energy method of COMSOL software. The electromagnetic field distribution is accurately calculated through finite element analysis to ensure that the inductor 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 satisfies the inductance and geometric constraints. If the calculated critical current does not satisfy the constraints, re-initialize the variables in S1 and repeat steps S1 to S3 until a structural parameter that satisfies the conditions is found.

[0022] Furthermore, in S3, the process of determining whether the calculated critical current meets 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 for the size, shape, and arrangement of the coil.

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

[0024] Initialize the population: Randomly generate a set of individuals, each representing 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 to obtain a fitness vector;

[0026] Pareto Front Ranking: Individuals are ranked according to their fitness vectors, and they are divided into different Pareto fronts to identify the non-dominated solution set;

[0027] Crowding distance calculation: In each Pareto front, the distance between each individual and its neighbors is calculated to maintain population diversity;

[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 Pareto front and crowding distance.

[0029] Crossover and mutation operations: Selected individuals are subjected to crossover and mutation operations to generate new individuals, which are then added to the next generation of the population;

[0030] Population renewal: Replacing existing individuals with new ones to form the next generation of the population;

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

[0032] Furthermore, in the superconducting toroidal hollow reactor, each coil is a double-pane coil, which is wound around once 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 using the genetic algorithm toolbox in MATLAB. The optimization algorithm is a multi-objective genetic algorithm, and the optimization objectives are to minimize the amount of strip material used and minimize AC loss.

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

[0035] Furthermore, in S6, 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: Based on AC losses, determine the cooling capacity of the refrigeration system, and calculate the purchase price, operating cost, refrigerant cost, and possible maintenance cost of the refrigeration system.

[0038] Total cost calculation: Add the calculated strip cost and cooling cost together, 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 refrigeration cost, the net refrigeration capacity of the refrigeration system must be greater than the AC loss and system heat leakage. The net refrigeration capacity of the refrigeration system is related to the refrigeration temperature. The lower the refrigeration temperature, the smaller the net refrigeration capacity, as shown in Figure 4.

[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-described method for optimizing the structure of a superconducting toroidal hollow reactor.

[0041] A third aspect of the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method for structural optimization of a superconducting toroidal hollow reactor. Beneficial effects

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

[0043] This invention optimizes the structural parameters of a superconducting toroidal hollow reactor using a multi-objective genetic algorithm, achieving significant economic benefits and performance improvements. First, a comprehensive evaluation of the reactor's electromagnetic performance and cost-effectiveness is conducted using a joint simulation platform of MATLAB and COMSOL, ensuring the accuracy and reliability of the design. Second, the optimization process considers the AC losses of the superconducting material, ensuring efficient operation of the reactor in the superconducting state and reducing operating costs. Furthermore, this invention comprehensively considers cooling costs, achieving effective control of the reactor's total cost through a precise cost calculation model, thus improving economic efficiency. Finally, through iterative optimization, the optimal structural parameters with the least amount of strip material and the lowest AC losses are found while meeting design specifications, thereby achieving performance optimization and cost minimization of the superconducting toroidal hollow reactor. Attached Figure Description

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

[0045] Figure 2 is an optimized flowchart of an embodiment of the present invention;

[0046] Figure 3 shows the optimization results of an embodiment of the present invention, where each point represents a set of solutions.

[0047] Figure 4 is a schematic diagram illustrating an example of the relationship between the net cooling capacity and the cooling temperature of a refrigeration system. Embodiments of the present invention

[0048] The purpose of this invention is to propose a structural optimization method for superconducting toroidal hollow reactors. Through joint simulation using MATLAB and COMSOL, the structural parameters of the superconducting reactor are calculated to achieve the lowest total cost and improve economic efficiency. This invention optimizes the structural parameters of the superconducting reactor using joint simulation with MATLAB and COMSOL, achieving the lowest total cost and improved economic efficiency. The optimization variables are the structural parameters of the reactor, including the inner diameter of the coil, the toroidal 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 AC losses, and minimize the total cost. The optimization algorithm adopts a multi-objective genetic algorithm. This 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, improving the economic efficiency of reactor design.

[0049] The superconducting toroidal air-core reactor is divided into three phases. Each single-phase reactor consists of multiple circular double-pane coils, which are uniformly arranged in a ring around the central axis with a certain radius, as shown in Figure 1. Here, R is the ring 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 a superconducting reactor is as follows: When the load in a line is small or the end is open, power frequency overvoltage will occur due to the capacitive effect of a long line. Since inductance and capacitance are out of phase, the operation of the reactor will compensate for the capacitive effect of the line, limit the rise of power frequency voltage in the system, and achieve local reactive power absorption. By selecting a suitable inductor to make the inductor and capacitor resonate in parallel, the capacitive effect is completely eliminated.

[0051] The present invention will now be described in detail 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 for the superconducting toroidal hollow reactor in this embodiment includes the following steps:

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

[0055] S2. Inductance Adjustment: Adjust the number of turns of the coil. Coarse adjustment is performed using the Newman formula in MATLAB, and fine adjustment is performed using the magnetic energy method in COMSOL, so that the inductance value meets the design specifications.

[0056] Specifically, the following steps are included:

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

[0058] S2-2. The inductor is finely adjusted using the magnetic energy method of COMSOL software. The electromagnetic field distribution is accurately calculated through finite element analysis to ensure that the inductor 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 they meet, continue to the next step.

[0060] Specifically, the following steps are included:

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

[0062] S3-2. Determine whether the calculated critical current satisfies the inductance and geometric constraints. If the calculated critical current does not satisfy the constraints, re-initialize the variables in S1 and repeat steps S1 to S3 until a structural parameter that satisfies the conditions is found.

[0063] Furthermore, in S3, the process of determining whether the calculated critical current meets 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 for 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 minimum strip material usage and the lowest AC loss is found.

[0066] Specifically, the following steps are included:

[0067] Initialize the population: Randomly generate a set of individuals, each representing 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 to obtain a fitness vector;

[0069] Pareto Front Ranking: Individuals are ranked according to their fitness vectors, and they are divided into different Pareto fronts to identify the non-dominated solution set;

[0070] Crowding distance calculation: In each Pareto front, the distance between each individual and its neighbors is calculated to maintain population diversity;

[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 Pareto front and crowding distance.

[0072] Crossover and mutation operations: Selected individuals are subjected to crossover and mutation operations to generate new individuals, which are then added to the next generation of the population;

[0073] Population renewal: Replacing existing individuals with new ones to form the next generation of the population;

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

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

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

[0077] S6. Cost Calculation: In the optimal solution set, calculate the cost of the strip and the cooling cost required to meet the AC loss based on the amount of strip material and AC loss. Combine the costs of other components of the superconducting reactor to obtain the total cost and find the solution with the lowest total cost in the optimal solution set.

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

[0079] In the superconducting toroidal hollow reactor, each coil is a double-pane coil, which is wound around once and connected in series and parallel with each other through metal parts, and finally divided into multiple parallel branches.

[0080] The working principle of this invention is based on a multi-objective genetic algorithm, which optimizes the structural parameters of a superconducting toroidal hollow reactor by simulating natural selection and genetic mechanisms. The algorithm initializes a population containing multiple potential solutions, each solution representing a set of structural parameters of the reactor. These parameters include the coil inner diameter, winding radius, number of coil turns, number of coils, and number of parallel branches, which together determine the reactor's performance, such as the amount of tape used and AC losses.

[0081] During the iteration process, the algorithm evaluates the fitness of each individual, i.e., its performance in a multi-objective function aimed at minimizing tape usage and AC loss. Through selection, crossover, and mutation operations, the population continuously evolves, gradually approaching the Pareto optimal front. The Pareto optimal front consists of a set of non-dominated solutions that provide the optimal trade-off among the multiple objectives.

[0082] Ultimately, the algorithm converges to an optimal solution set, representing the reactor structural parameters that achieve the lowest cost while satisfying design constraints. These parameters consider not only the physical properties of the superconducting material but also cooling and manufacturing costs, ensuring the reactor's economy and efficiency in practical applications. Using the method of this invention, designers can quickly find the reactor design best suited for specific application requirements, thereby improving the performance and reducing the cost of superconducting reactors.

[0083] In specific implementation, the present invention will be described using the following process as an example:

[0084] Figure 2 illustrates 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 used and the AC loss; and the optimization method employs 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 in the reactor coil to achieve an inductance of 0.318H, meeting the design specification of 1Mvar. This is divided into coarse adjustment and fine adjustment. Coarse adjustment calculates the inductance using the Newman formula in MATLAB, while fine adjustment calculates the inductance using the COMSOL magnetic energy method.

[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 they do, continue to the next step.

[0088] 4. Calculate the amount of material used in the reactor and the AC loss using an equivalent COMSOL model. Once the population generation reaches a set value, output the optimal solution set.

[0089] Figure 3 shows the optimization results, with the coordinate axes representing the two optimization objectives. Each point represents a feasible solution, and the red points indicate the optimal solution set. Based on engineering experience, an economic analysis was performed on the optimal solution set, calculating the cost of the strip material and the 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 toroidal hollow reactor.

[0091]

[0092] Example 2

[0093] This embodiment provides a computer-readable storage medium storing a specific computer program. When executed by a processor, this program can implement the various steps of the structural optimization method for the superconducting toroidal hollow reactor described above. This storage medium can be any form of computer-readable medium, such as a hard disk, CD-ROM, DVD, flash drive, ROM, RAM, or a digital signal transmitted via a computer network.

[0094] This computer program contains a series of instructions designed to guide the processor in optimizing the structural parameters of a superconducting reactor. The program first initializes the reactor's initial structural parameters, then adjusts the inductance using simulation software, calculates the critical current, and determines whether inductance and geometric constraints are met. If satisfied, the program proceeds to cost calculations, including tape usage, AC losses, and cooling costs. Subsequently, the program uses a multi-objective genetic algorithm for iterative optimization until the optimal solution set with the lowest cost is found. Finally, the program outputs the optimal solution set, including parameters such as coil inner diameter, winding radius, and number of coil turns, along with the corresponding critical current, inductance value, tape usage, AC losses, and total cost. This storage medium allows any user with the appropriate hardware to optimize the structure of a superconducting toroidal hollow reactor by running the program, 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. This computer program is designed to execute a structural optimization method for superconducting toroidal hollow reactors. When the program runs on a computer system's processor, it can automatically execute a series of predetermined optimization steps. These steps include initializing the reactor's structural parameters, adjusting the number of coil turns to meet specific inductance design specifications, calculating the critical current and verifying compliance with inductance and geometric constraints, calculating the amount of strip material used and AC losses, and comprehensively considering cooling costs to calculate the total cost. Through a multi-objective genetic algorithm, the program can iteratively find and determine the optimal solution set, which achieves the goals of minimizing strip material usage and AC losses 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 provided to enable those skilled in the art to understand and use the invention. It will be apparent to those skilled in the art that various modifications can be made to these embodiments, and the general principles described herein can be applied to other embodiments without inventive effort. Therefore, the present invention is not limited to the above embodiments, and any 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 invention should be within the protection scope of the present invention.

Claims

1. A method for optimizing the structure of a superconducting toroidal hollow reactor, characterized by, Includes the following steps: S1. Initialization: Set the initial structural parameters of the superconducting reactor, including coil inner diameter, winding radius, number of coil turns, number of coils, and number of parallel branches; S2. Inductance Adjustment: Adjust the number of turns of the coil. Coarse adjustment is performed using the Newman formula in MATLAB, and fine adjustment is performed using the magnetic energy method in COMSOL, so that the inductance value meets the design specifications. 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 they meet, 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 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 minimum strip material usage and the lowest AC loss is found. S6. Cost Calculation: In the optimal solution set, calculate the cost of the strip and the cooling cost required to meet the AC loss based on the amount of strip material used and AC loss. Combine the costs of other components of the superconducting reactor to obtain the total cost and find the solution with the lowest total cost in the optimal solution set. S7. Output Results: Output the optimal solution, including coil inner diameter, winding radius, number of coil turns, number of coils, number of parallel branches, and the corresponding critical current, inductance value, tape usage, AC loss, and total cost.

2. The method for structural optimization of a superconducting toroidal- shaped air-core reactor according to claim 1, characterized in that, S2 specifically includes the following steps: S2-1. First, the number of coil turns is roughly adjusted using the Newman formula in MATLAB software to quickly obtain an inductance value close to the design requirements. S2-2. The inductor is finely adjusted using the magnetic energy method of COMSOL software. The electromagnetic field distribution is accurately calculated through finite element analysis to ensure that the inductor value accurately meets the design specifications.

3. The method for structural optimization of a superconducting toroidal volume 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 satisfies the inductance and geometric constraints. If the calculated critical current does not satisfy the constraints, re-initialize the variables in S1 and repeat steps S1 to S3 until a structural parameter that satisfies the conditions is found.

4. The method for structural optimization of a superconducting toroidal- shaped air-core reactor according to claim 3, characterized in that, In S3, the process of determining whether the calculated critical current meets 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, including the design requirements for the size, shape, and arrangement of the coil.

5. The method for structural optimization of a superconducting toroidal volume reactor according to claim 1, characterized in that, S5 specifically includes the following steps: Initialize the population: Randomly generate a set of individuals, each representing 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 to obtain a fitness vector; Pareto Front Ranking: Individuals are ranked according to their fitness vectors, and they are divided into different Pareto fronts to identify the non-dominated solution set; Crowding distance calculation: In each Pareto front, the distance between each individual and its neighbors is calculated to maintain population diversity; Selection operation: Select a group of individuals from the population to generate the next generation of individuals. The selection strategy is usually based on Pareto front and crowding distance. Crossover and mutation operations: Selected individuals are subjected to crossover and mutation operations to generate new individuals, which are then added to the next generation of the population; Population renewal: Replacing existing individuals with new ones to form the next generation of the population; Iterate until convergence: Repeat the above steps until the number of iterations is satisfied or a satisfactory solution set is found, which is the optimal solution set with the lowest total cost and the lowest communication loss.

6. The method for structural optimization of a superconducting toroidal volume reactor according to claim 1, characterized in that, In the superconducting toroidal hollow reactor, each coil is a double-pane coil, which is wound around once and connected in series and parallel with each other through metal parts, and finally divided into multiple parallel branches.

7. The method for structural optimization of a superconducting toroidal volume reactor according to claim 1, characterized in that, In S5, the structural parameters of the reactor are optimized using the genetic algorithm toolbox in MATLAB. The optimization algorithm is a multi-objective genetic algorithm, and the optimization objectives are to minimize the amount of strip material used and minimize AC loss.

8. The method for structural optimization of a superconducting toroidal volume reactor according to claim 1, characterized in that, In S2 to S4, the inductance and AC loss of the reactor are calculated using the equivalent simplified model in COMSOL.

9. A computer readable storage medium having stored thereon a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the structural optimization method for the superconducting toroidal hollow reactor as described in any one of claims 1 to 8.

10. A computer program product comprising a computer program, characterized in that, When executed by a processor, the computer program implements the structural optimization method for the superconducting toroidal hollow reactor as described in any one of claims 1 to 8.

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