A multi-objective optimization method, device and medium for superconducting cable structural parameters

Abstract

The present invention relates to a multi-objective optimization method, device and medium for superconducting cable structural parameters, comprising the following steps: S1, obtaining superconducting cable structural parameters and performance parameters, setting the constraint range of each structural parameter of the superconducting cable, constructing an objective function based on the superconducting cable structural parameters and performance parameters, and establishing a multi-objective optimization model for superconducting cable structural parameters; S2, iteratively solving the multi-objective optimization model for superconducting cable structural parameters through an improved multi-objective grey wolf optimization algorithm to obtain the optimal solution for the superconducting cable structural parameters; wherein, a weight coefficient negatively correlated with the overall sensitivity index of each structural parameter of the superconducting cable is assigned to the iteration coefficient in the multi-objective grey wolf optimization algorithm to obtain the improved multi-objective grey wolf optimization algorithm. Compared with the prior art, the present invention can further improve the optimization speed and optimization effect of superconducting cable structural parameters.

Description

Technical Field

[0001] The invention belongs to the technical field of power transmission and distribution, and in particular relates to a multi-objective optimization method, equipment and medium for superconducting cable structural parameters. Background Art

[0002] During operation, the superconducting cable body will generate hysteresis loss due to the magnetic field transformation caused by the AC current. In order to maintain the normal operating temperature of the superconducting cable, the cooling system needs to consume at least 15 times the electrical energy to remove the heat generated by this part of the AC loss from the system. Therefore, reducing the AC loss by optimizing the cable structure and then controlling the system cooling cost is an important factor to be considered in the design of the superconducting cable structure. In addition to affecting the cooling cost, the optimization of the cable structure also directly affects the amount of superconducting tape used. The production and preparation cost of superconducting tape is relatively high, so it is also very important to reasonably control the amount of tape used. Studies have shown that increasing the tape winding angle can reduce AC loss, but it will also increase the amount of tape used. In order to obtain the optimal superconducting cable structure, it is necessary to balance multiple objective functions.

[0003] Chinese patent application CN202210369373.0 discloses a method for rapid optimization of the main structure of a superconducting cable. The particle swarm algorithm is used to quickly optimize the main structural parameters of the cold-insulated high-temperature superconducting cable, and the various parameters of the main structure of the high-temperature superconducting cable can be accurately obtained, which improves the research and development efficiency and accuracy of the high-temperature superconducting cable. Although the particle swarm algorithm performs well in terms of convergence speed, when dealing with large-scale optimization problems, the convergence speed of the algorithm may be affected due to the need to calculate the speed and position of a large number of particles; in addition, during the search process of the particle swarm algorithm, if the particles in the group converge to the vicinity of the local optimal solution too early, especially when dealing with complex multi-peak function optimization problems, the entire group may fall into the local optimal solution and fail to find the global optimal solution. The multi-objective gray wolf optimization algorithm (MOGWO algorithm) that simulates the hunting behavior of gray wolf groups focuses on maintaining the diversity of the solution space during the optimization process, and is easy to understand and apply. It is often used to deal with complex optimization problems such as superconducting cable structure optimization with multiple parameters and multiple objectives. However, when using the MOGWO algorithm to process the superconducting cable structure optimization model, the more layers of tape, the more parameters involved, the more tedious the algorithm iteration screening process, and the calculation time will increase exponentially. Therefore, it is necessary to improve the MOGWO algorithm to improve its convergence speed and optimization effect when solving the superconducting cable structure parameter optimization problem. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a multi-objective optimization method, device and medium for superconducting cable structural parameters, so as to improve the optimization speed and optimization effect of superconducting cable structural parameters.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] A multi-objective optimization method for superconducting cable structural parameters comprises the following steps:

[0007] S1. Obtaining structural parameters and performance parameters of a superconducting cable, setting constraint ranges for various structural parameters of the superconducting cable, constructing an objective function based on the structural parameters and performance parameters of the superconducting cable, and establishing a multi-objective optimization model for structural parameters of the superconducting cable;

[0008] S2. Iteratively solving the multi-objective optimization model of the superconducting cable structural parameters by using an improved multi-objective grey wolf optimization algorithm to obtain an optimal solution for the superconducting cable structural parameters;

[0009] Among them, a weight coefficient negatively correlated with the overall sensitivity index of each structural parameter of the superconducting cable is assigned to the iteration coefficient in the multi-objective grey wolf optimization algorithm, thereby obtaining the improved multi-objective grey wolf optimization algorithm.

[0010] Furthermore, the structural parameters of the superconducting cable include the number of tapes in each layer of the superconducting cable, the winding angle of each layer and the radius of the innermost conductive layer.

[0011] Furthermore, the objective function includes the AC loss of the superconducting cable and the length of the superconducting tape.

[0012] Furthermore, the iteration coefficients in the multi-objective grey wolf optimization algorithm include one or more of the individual position contraction and expansion coefficient A and the individual's active exploration degree C within a certain random range around itself.

[0013] Furthermore, the multi-objective optimization model of the superconducting cable structural parameters is analyzed by the Sobol analysis method to obtain the overall sensitivity index of each structural parameter of the superconducting cable.

[0014] Furthermore, the multi-objective optimization model of superconducting cable structural parameters includes multiple objective functions, and Sobol analysis is performed on each objective function to obtain the overall sensitivity index of each structural parameter of the superconducting cable under each objective function, and the weight coefficient is generated based on the inverse of the average value of the overall sensitivity index of all objective functions.

[0015] Furthermore, the specific process of iteratively solving the multi-objective optimization model of the superconducting cable structure parameters by using the improved multi-objective grey wolf optimization algorithm is as follows:

[0016] S201, randomly generate an initial population, perform non-dominated sorting on the initial population, and establish a non-dominated solution set Archive;

[0017] S202, updating the iteration coefficient in the multi-objective grey wolf optimization algorithm based on the weight coefficient generated by the overall sensitivity index of each structural parameter of the superconducting cable;

[0018] S203, updating the position of each individual in the population based on the iteration coefficient, and updating the non-dominated solution set Archive;

[0019] S204, determine whether the iteration termination condition is met, if yes, proceed to step S205; if no, return to step S203;

[0020] S205, outputting a non-dominated solution set Archive, solving the Euclidean distance after the fitness of each non-dominated solution is normalized, and selecting the non-dominated solution with the smallest Euclidean distance as the optimal solution to output.

[0021] Furthermore, in step S204, the iteration termination condition is reaching a preset maximum number of iterations.

[0022] The present invention also provides an electronic device, comprising a memory, a processor, and a program stored in the memory, wherein the processor implements the above method when executing the program.

[0023] The present invention also provides a computer-readable storage medium on which a computer program is stored, and the program implements the above method when executed by a processor.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] 1. The present invention assigns a weight coefficient that is negatively correlated with the overall sensitivity index of each structural parameter of the superconducting cable to the iteration coefficient in the multi-objective gray wolf optimization algorithm, and obtains an improved multi-objective gray wolf optimization algorithm to solve the multi-parameter, multi-objective complex optimization problem of superconducting cable structural parameter optimization, so that the superconducting cable structural parameters that have a greater impact on the objective function use a smaller iteration coefficient during the iteration process to improve the search accuracy within the constraint range and avoid missing the optimal solution; at the same time, the superconducting cable structural parameters that have a smaller impact on the objective function use a larger iteration coefficient during the iteration process to more quickly cover the entire constraint space, speed up the optimization speed, and avoid falling into the local optimal solution; the improved multi-objective gray wolf optimization algorithm performs personalized iterations for different superconducting cable structural parameters, which can significantly improve the convergence speed and optimization effect of the multi-objective gray wolf optimization algorithm when solving the multi-objective superconducting cable structural parameter optimization problem.

[0026] 2. The present invention analyzes the multi-objective optimization model of superconducting cable structural parameters through the Sobol analysis method to obtain the overall sensitivity index of each structural parameter of the superconducting cable, which can effectively determine the key structural parameters that affect the performance of the multi-objective optimization model of superconducting cable structural parameters, and analyze the interaction effects between the structural parameters, which is convenient for understanding and optimizing complex nonlinear multi-objective models. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a flow chart of the method of the present invention;

[0028] Figure 2 Flowchart of the improved multi-objective gray wolf optimization algorithm;

[0029] Figure 3 This is the result diagram of Sobol analysis of AC loss;

[0030] Figure 4 This is the Sobol analysis result diagram of strip length;

[0031] Figure 5 This is a graph showing the convergence of the multi-objective grey wolf optimization algorithm before and after optimization of different iteration coefficients.

[0032] Among them, (5a) represents the unoptimized situation, (5b) represents the situation where only the individual position contraction and expansion coefficient A is optimized, (5c) represents the situation where only the individual's active exploration degree C within a certain random range around itself is optimized, and (5d) represents the situation where both the individual position contraction and expansion coefficient A and the individual's active exploration degree C within a certain random range around itself are optimized. DETAILED DESCRIPTION

[0033] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0034] Example 1

[0035] This embodiment provides a multi-objective optimization method for superconducting cable structural parameters, and optimizes the structural parameters of a 35kV / 2.2kA three-phase turnkey superconducting cable. Figure 1 As shown, the following steps are included:

[0036] S1. Obtain the structural parameters and performance parameters of the superconducting cable, set the constraint range of each structural parameter of the superconducting cable, construct the objective function based on the structural parameters and performance parameters of the superconducting cable, and establish a multi-objective optimization model for the structural parameters of the superconducting cable.

[0037] The 35kV / 2.2kA three-phase turnkey superconducting cable contains 4 layers of superconducting tapes, which are superconducting tape-shielding layer, insulating layer, superconducting tape-conducting layer and semi-conducting layer from outside to inside. In this embodiment, the number of tapes in each layer is set to n1, n2, n3, and n4, and the winding angles of each layer are θ1, θ2, θ3, and θ4, respectively. The radius of the innermost layer is R, with a total of 9 structural parameters. The superconducting cable AC loss Q and the superconducting tape length Length are used as two objective functions to establish a multi-objective optimization model for superconducting cable structural parameters. The specific calculation formulas of the two objective functions are as follows:

[0038] Q=Q N +Q mag

[0039]

[0040] i ac =I / I c

[0041]

[0042]

[0043]

[0044] Among them, Q N is the self-field transmission loss of the superconducting tape, N i is the number of strips per layer, f is the frequency, μ0 is the vacuum permeability, I is the strip load current, I c is the critical current of the superconducting tape, i ac is the normalized current, Q mag is the external field magnetization loss of the superconducting cable, B i is the magnetic induction intensity, β i Normalized magnetic field, S i is the cross-sectional area of ​​the superconducting tape, J C is the critical current density of the superconducting tape, b is half of the width of the superconducting tape, L0 is the cable length, θ i is the winding angle of the i-th layer.

[0045] The calculation results are then compared in the form of Euclidean distance to select the optimal solution:

[0046]

[0047] Due to the limitation of tape stress, the winding angles θ1, θ2, θ3, and θ4 of each layer are set in the range of 5°-35°; due to the limitation of the cross-sectional area of ​​the copper skeleton of the superconducting cable, the winding radius R of the innermost tape is set in the range of 11.45mm-12.45mm; due to the limitation of the width and critical current density of the superconducting tape under a certain winding radius, the number of tape roots n1, n2, n3, and n4 in each layer are set in the range of ([11,14], [11,14], [19,22], [20,23]) respectively.

[0048] S2. The multi-objective optimization model of superconducting cable structural parameters is iteratively solved by the improved multi-objective grey wolf optimization algorithm to obtain the optimal solution of the superconducting cable structural parameters.

[0049] In the multi-objective gray wolf optimization algorithm MOGWO, the core iterative process (the process of encircling prey in the hunting behavior of gray wolf groups) is the process of adjusting the positions X of other individuals based on the positions of the three optimal leader solutions α, β, and δ. The iterative process of adjusting the individual position X based on the α solution position is taken as an example (the iterative process based on the β and δ solutions is the same, only the subscript is changed), as shown in the following formula:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] Where D represents the distance between the individual and the location of the α solution, t is the iterative number, and t max is the maximum number of iterations, which is set to 300 in this embodiment. α (t) is the position of the α solution in the tth generation, X(t) is the position of other individuals to be solved in the tth generation, a is the convergence factor, which decreases linearly from 2 to 0 as the number of iterations increases, r1 and r2 are random numbers between [0,1], so A is a coefficient representing the contraction and expansion of the individual position, and its range is [-2,2]. That is, when |A|>1, the individual will move away from the α wolf position, and when |A|<1, the individual will move closer to the α wolf position, that is, the first half of the optimization tends to search the entire space, and the second half tends to converge to the optimal solution. C represents the degree of active exploration of the individual within a certain random range around itself.

[0056] The next positions of the three leaders α, β, and δ are combined to update the next generation positions X(t+1) of other individuals, as shown in the following formula:

[0057]

[0058] It can be seen from the above formula that for each structural parameter in the superconducting cable, the iteration coefficients A and C in the iteration process are the same value, and the global search is also performed with the same step size. However, in the study of the influence of a single variable of a superconducting cable on the AC loss, it is found that the influence of different parameters on the AC loss varies. Therefore, the iteration process should also be adjusted differently based on the sensitivity of different parameters. The present invention uses the normalized overall sensitivity of each parameter obtained by Sobol analysis to assign weight coefficients to the iteration coefficients in the random iteration process, as shown in the following formula:

[0059]

[0060]

[0061] Among them, S T1 , S T2 ,……,S Tn Represents the normalized overall sensitivity index of each parameter.

[0062] The Sobol analysis method is used to analyze the multi-objective optimization model of superconducting cable structural parameters, and the sensitivity analysis results under the two objective functions are as follows: Figure 2 and Figure 3 As shown. It can be seen that in the two-objective function calculation model, the first-order sensitivity index distribution of the 9 input structural parameters is relatively disordered due to the high nonlinearity in the calculation process. The overall sensitivity index of the structural parameters in the two-objective function calculation model generally shows a trend of gradual increase. This shows that when considering the interaction and nonlinear relationship between the parameters, the calculation model has made a more comprehensive and specific response to different parameters: the number of superconducting tapes in each layer generally affects the AC loss more significantly than the winding angle of each layer. Therefore, the average value of the overall sensitivity index of the two objective functions is taken as the optimization basis for the formula coefficients, as follows:

[0063]

[0064]

[0065] Through the above adjustments, the parameters that have a greater impact on the objective function can use smaller random values ​​during the iteration process to improve the search accuracy of the parameters within the constraint range and avoid missing the optimal solution; at the same time, the parameters that have a smaller impact on the objective function can use larger random values ​​during iteration to cover the entire constraint space more quickly, thereby speeding up the optimization process and avoiding falling into the local optimal solution.

[0066] The optimized MOGWO algorithm process is as follows: Figure 4As shown, the specific process of iteratively solving the multi-objective optimization model of the superconducting cable structure parameters by using the improved multi-objective grey wolf optimization algorithm is as follows:

[0067] S201, randomly generate an initial population, perform non-dominated sorting on the initial population, discard dominated solutions, retain non-dominated solutions, and establish a non-dominated solution set Archive;

[0068] S202, updating the iteration coefficient in the multi-objective grey wolf optimization algorithm based on the weight coefficient generated by the overall sensitivity index of each structural parameter of the superconducting cable;

[0069] S203, updating the position of each individual in the population based on the iteration coefficient, and updating the non-dominated solution set Archive;

[0070] S204, determine whether the maximum number of iterations has been reached, if so, proceed to step S205; if not, return to step S203;

[0071] S205, outputting a non-dominated solution set Archive, solving the Euclidean distance after the fitness of each non-dominated solution is normalized, and selecting the non-dominated solution with the smallest Euclidean distance as the optimal solution to output.

[0072] The improved algorithm performs personalized iterations for different superconducting cable structural parameters, which can significantly improve the convergence speed and optimization effect of the MOGWO algorithm in solving the multi-objective superconducting cable structural parameter optimization problem. To verify the effectiveness of the method of the present invention, the convergence and iteration effects of the traditional MOGWO algorithm (coefficients A and C are not optimized), only optimizing coefficient A, only optimizing coefficient C, and optimizing coefficients A and C at the same time are compared. The results are as follows: Figure 5 As shown in (5a), (5b), (5c) and (5d), due to the limitation of random numbers in the intelligent optimization algorithm, the speed of iterative convergence to the optimal solution and the optimal solution converged to may be different in each optimization process, so the structural parameter optimization is performed three times in each case. It can be seen that the number of iterations of the optimal solution converged by the traditional MOGWO algorithm is distributed between 120 and 200; after optimizing the coefficient A three times, the number of iterations of the optimal solution converged by the optimization program is stably distributed below 50, the program convergence speed is greatly improved and the convergence effect is good; after optimizing the coefficient C three times, the convergence speed of the program is not optimized, and it cannot even converge to the optimal solution, and the optimization effect is poor; after optimizing the coefficients A and C three times at the same time, the number of iterations of the optimal solution converged by the optimization program is distributed between 100 and 200, the convergence speed improvement effect is not significant and the optimization effect is unstable. From the above comparison, it can be seen that optimizing the coefficient A in the MOGWO algorithm optimization program can significantly improve the convergence speed and optimization effect of the MOGWO algorithm.

[0073] In order to verify the accuracy of the convergence results of the proposed MOGWO algorithm based on the improved coefficient A, the optimization results obtained by the MOGWO algorithm with the improved coefficient A are compared with the 35kV / 2.2kA three-phase all-in-one superconducting cable structure in operation in the existing literature (Zhang Xize, Zong Xihua, Huang Yijia. Design research of kilometer-level superconducting cables in Shanghai [J]. Cryogenics and Superconductivity, 2022, 50(06): 35-41). The results are shown in Table 1.

[0074] Table 1 Structural parameters of three-phase turnkey superconducting cable before and after optimization

[0075]

[0076] As can be seen from Table 1, in general, the structural parameters obtained by the improved MOGWO algorithm based on the optimization coefficient A are not much different from the structural parameters of the three-phase all-in-one superconducting cable obtained in the existing literature (i.e., the reference values ​​in the table). In summary, based on the traditional MOGWO algorithm processing nonlinear multi-objective models, the present invention assigns a weight coefficient based on parameter sensitivity to its iteration coefficient A, which helps the global optimization algorithm to explore space and actively converge, thereby finding the global optimal solution faster and better, and can significantly improve the optimization speed and optimization effect in practical optimization problems with multiple parameters and multiple objectives.

[0077] Example 2

[0078] This embodiment provides an electronic device, including one or more processors and a memory, wherein one or more programs are stored in the memory, and instructions for executing all or part of the steps of the multi-objective optimization method for superconducting cable structural parameters as described in Example 1 can be executed.

[0079] 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 multi-objective optimization method for superconducting cable structural parameters, characterized in that: The following steps are involved: S1. Obtaining structural parameters and performance parameters of a superconducting cable, setting constraint ranges of various structural parameters of the superconducting cable, constructing objective functions based on the structural parameters and performance parameters of the superconducting cable, and establishing a multi-objective optimization model of superconducting cable structural parameters including multiple objective functions; S2. Iteratively solving the multi-objective optimization model of the superconducting cable structural parameters by using an improved multi-objective grey wolf optimization algorithm to obtain an optimal solution for the superconducting cable structural parameters; Wherein, a weight coefficient negatively correlated with the overall sensitivity index of each structural parameter of the superconducting cable is assigned to the iteration coefficient A and / or C in the multi-objective grey wolf optimization algorithm, thereby obtaining the improved multi-objective grey wolf optimization algorithm; The specific process of generating the weight coefficient is: Performing Sobol analysis on each objective function in the multi-objective optimization model of superconducting cable structural parameters to obtain a normalized overall sensitivity index of each structural parameter of the superconducting cable under each objective function; The average value of the normalized overall sensitivity index of each structural parameter of the superconducting cable under all objective functions is calculated, and the weight coefficient is generated according to the reciprocal thereof.

2. A multi-objective optimization method for superconducting cable structural parameters according to claim 1, characterized in that: The structural parameters of the superconducting cable include the number of tapes in each layer of the superconducting cable, the winding angle of each layer and the radius of the innermost conductive layer.

3. A multi-objective optimization method for superconducting cable structural parameters according to claim 1, characterized in that: The objective function includes the superconducting cable AC loss and the superconducting tape length.

4. The multi-objective optimization method for superconducting cable structural parameters according to claim 1, characterized in that: The iteration coefficients in the multi-objective grey wolf optimization algorithm include one or more of the individual position contraction and expansion coefficient A and the individual's active exploration degree C within a certain random range around itself.

5. The multi-objective optimization method for superconducting cable structural parameters according to claim 1, characterized in that: The specific process of iteratively solving the multi-objective optimization model of the superconducting cable structure parameters by using the improved multi-objective Grey Wolf optimization algorithm is as follows: S201, randomly generate an initial population, perform non-dominated sorting on the initial population, and establish a non-dominated solution set Archive; S202, updating the iteration coefficient in the multi-objective grey wolf optimization algorithm based on the weight coefficient generated by the overall sensitivity index of each structural parameter of the superconducting cable; S203, updating the position of each individual in the population based on the iteration coefficient, and updating the non-dominated solution set Archive; S204, determine whether the iteration termination condition is met, if yes, proceed to step S205; if no, return to step S203; S205, outputting a non-dominated solution set Archive, solving the Euclidean distance after the fitness of each non-dominated solution is normalized, and selecting the non-dominated solution with the smallest Euclidean distance as the optimal solution to output.

6. A multi-objective optimization method for superconducting cable structural parameters according to claim 5, characterized in that: In step S203, the iteration termination condition is reaching a preset maximum number of iterations.

7. An electronic device comprising a memory, a processor, and a program stored in the memory, characterized in that: When the processor executes the program, the method according to any one of claims 1 to 6 is implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

Images