Multi-objective optimization method for circular wireless charging coil of electric vehicle

Abstract

A multi-objective optimization method for a circular wireless charging coil of an electric vehicle comprises the following steps: constructing an equivalent circuit model of an S-S type resonance compensation topological structure of a wireless power transmission system, and carrying out alternating current impedance analysis on the equivalent circuit model to obtain an expression of system output power and transmission efficiency; determining an optimization target according to the derived system output power and transmission efficiency expression; building a circular wireless charging coil model, determining a wireless charging coil design variable needing to be optimized, and determining a constraint condition; and carrying out parameter optimization by adopting an improved multi-target samson swarm algorithm to obtain optimal design parameters of the wireless charging coil of the wireless power transmission system. According to the method, the problem that the transmission power and efficiency of the wireless power transmission system are unstable when a coupling mechanism of the wireless power transmission system deviates is solved; the optimized wireless charging coil can effectively improve the stability of wireless charging of the electric vehicle.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless power transmission, and in particular to a multi-objective optimization method for a circular wireless charging coil of an electric vehicle. Background Art

[0002] Since its introduction, wireless power transfer (WPT) technology has gradually surpassed traditional contact-based charging methods due to its high reliability, flexibility, and environmentally friendly features. With in-depth research, WPT has been widely adopted in a variety of fields, including mobile phones, electric vehicles (EVs), medical implants, and underwater vehicles, and is considered a major trend in the development of future charging technologies. Currently, theoretical research on WPT technology is relatively mature, with a primary focus on optimizing system performance, including improving key metrics such as power, transmission efficiency, and transmission distance.

[0003] However, WPT technology still faces many challenges in practical applications. For example, during wireless charging of electric vehicles, if the transmitting coil and receiving coil are misaligned, the system's transmission power efficiency will decrease. In addition, existing technologies still have shortcomings in constant current / constant voltage output, load change adaptability, and dynamic charging capabilities. These issues limit the application of WPT technology in practical scenarios. To fully realize the potential of wireless power transmission technology, further research is needed to address these practical challenges. For example, improving coil design, optimizing circuit topology, introducing adaptive control strategies, and adopting new materials and technologies can effectively enhance system transmission efficiency and stability. At the same time, attention must also be paid to system safety, electromagnetic compatibility, and environmental impact. Summary of the Invention

[0004] This paper proposes a multi-objective optimization method for circular wireless charging coils for electric vehicles. This method addresses the instability of wireless power transmission system transmission power and efficiency when the coupling mechanism of the wireless power transmission system is offset. The optimized wireless charging coil effectively improves the stability of wireless charging in electric vehicles.

[0005] The technical solution adopted by the present invention is: A multi-objective optimization method for a circular wireless charging coil for an electric vehicle comprises the following steps: Step 1: Construct an equivalent circuit model of the SS-type resonant compensation topology structure of the wireless power transmission system, perform AC impedance analysis on it, and obtain the expressions of system output power and transmission efficiency; Step 2: Determine the optimization target based on the derived system output power and transmission efficiency expressions; Step 3: Build a circular wireless charging coil model, determine the wireless charging coil design variables that need to be optimized, and determine the constraints; Step 4: Use the improved multi-objective sand cat swarm algorithm to perform parameter optimization and obtain the optimal design parameters of the wireless charging coil of the wireless power transmission system.

[0006] In the step 1, constructing an equivalent circuit model of the SS-type resonant compensation topology structure of the wireless power transmission system specifically includes: The primary side is the high-frequency AC power output by the inverter , compensation capacitor , primary coil self-inductance , primary equivalent resistance Series structure; The secondary side is determined by the self-inductance of the secondary coil , compensation capacitor , load equivalent resistance , secondary side equivalent resistance Series structure; The mutual inductance between the primary coil and the secondary coil is ; The currents flowing through the primary and secondary sides are 、 .like Figure 1 shown.

[0007] The system output power expression is: (1); In formula (1), is the output power, is the system resonant angular frequency.

[0008] Assume that the coupling coefficient between the primary and secondary coils is , then the self-inductance and mutual inductance of the primary and secondary sides satisfy the expression: (2); Then the system output power expression can be transformed into: (3); Quality factor of primary and secondary coils 、 The expression is: (4); (5); Then the system transmission efficiency satisfies: (6); In formula (6), Indicates the system transmission efficiency, is the input power.

[0009] From the expression of output power and transmission efficiency, it can be seen that increasing the system coupling coefficient can improve power and efficiency, so the coupling coefficient is As the first optimization goal, Satisfies the formula: (7); Where, is the coupling coefficient, is the mutual inductance of the primary and secondary coils, is the self-inductance of the primary coil, is the self-inductance of the secondary coil.

[0010] In order to obtain a suitable Pareto frontier, the objective function is inversely expressed as: (8); On the other hand, for electric vehicle wireless charging, anti-drift performance is an important factor to consider. Therefore, the offset reduction rate in different directions is defined to measure the system anti-drift performance. The formula is as follows: (9); (10); (11); In the above formula, is the x-direction offset drop rate; is the y-direction offset decrease rate; is the rate of decrease of the offset in the z direction; is the coupling coefficient when the coils are facing each other; is the x-direction offset rate; is the y-direction offset rate; is the offset rate in the z direction.

[0011] Since the wireless charging coil is a symmetrical coil and the electric vehicle is mainly affected by the offset in the x and y directions when charging, the second optimization goal of the wireless charging coil structure is set as the comprehensive offset reduction rate, which is expressed as follows: (12); In formula (12), Indicates the comprehensive offset decrease rate.

[0012] In step 2, two optimization objectives are selected: (13); In formula (11), is the number of turns of the primary coil, is the primary coil wire diameter, is the primary coil turn spacing, is the number of turns of the secondary coil, is the secondary coil wire diameter, is the secondary coil turn spacing; represents the objective function 1 with respect to the above parameters, represents the objective function 2 with respect to the above parameters.

[0013] In step 3, a circular wireless charging coil model is constructed, such as Figure 6 As shown. Determine the number of turns of the primary coil , Primary coil wire diameter , primary coil turn spacing , secondary coil turns , secondary coil wire diameter , secondary coil turn spacing is the design variable to be optimized.

[0014] Determination of constraints, including: According to the national standard GB / T38775.6-2021, using the MF-WPT1 Z2 vehicle as a reference, the recommended maximum outer diameter (diameter) for the transmitting coil is 650mm, and the recommended maximum outer diameter (diameter) for the receiving coil is 160mm. The maximum lateral offset distance must be no less than 100mm, and the maximum longitudinal offset distance must be no less than 70mm. Therefore, this invention fixes the outer diameter of the transmitting coil at 650mm and the outer diameter of the receiving coil at 160mm. The longitudinal transmission distance is 140mm-210mm, and the initial transmission distance is 140mm.

[0015] The coil size must meet the following requirements: the inner diameter must not be less than the sum of the wire diameter and the turn spacing. The size constraints are: (14); In formula (14), It is expressed as the difference between the inner diameter of the primary coil and the wire diameter and the turn spacing; It is expressed as the difference between the inner diameter of the secondary coil and the wire diameter and the turn spacing; is the radius of the primary coil; is the radius of the secondary coil; Indicates the inner diameter of the primary coil; Indicates the inner diameter of the secondary coil.

[0016] In step 4, the improved multi-objective sand cat swarm algorithm is as follows: in the original multi-objective sand cat swarm algorithm, the global optimal solution is selected according to the two-stage similarity distance, and the particles in the population are guided to seek the optimal solution to improve the uniformity of the Pareto solution; the improved multi-objective sand cat swarm algorithm includes the following steps: S4.1: Initialize the population, including the number of sand cats N and the maximum number of iterations And the position of each sand cat Pos(i), the formula satisfies: (15); In formula (15), L is the lower bound of the search space, which is a D-dimensional vector; U is the lower bound of the search space, which is a D-dimensional vector; is a D-dimensional random vector with each component uniformly distributed between [0,1].

[0017] S4.2: Calculate and store the fitness value corresponding to each sand cat's position, where the fitness value satisfies: (16); In formula (16), is the fitness value of the i-th sand cat, which is an M-dimensional vector; M is the number of objective functions.

[0018] Among them, the position of the sand cat with the largest fitness value is the current optimal sand cat position , optimal sand cat position Satisfies the formula: (17); In formula (17), arg min is the instruction that returns the parameter (position) that minimizes the function value; Archive is the external archive.

[0019] S4.3: Determine the fitness value of each sand cat position and perform Pareto sorting. The specific logic is: S4.3.1: Traverse all sand cat locations in the population and compare dominance relationships between them; S4.3.2: Classify non-dominated levels according to dominance relationships (Rank): Rank 1: individuals that are not dominated by any solution; Rank 2: Individuals that are dominated only by Rank 1 individuals, and so on.

[0020] S4.3.3: Store all Rank 1 individuals in an external archive.

[0021] S4.4: Use similarity distance in two stages to select the global optimal solution in the external archive; S4.5: Determine whether the algorithm meets the termination condition: The Pareto front converges (the improvement of the solution set is lower than the threshold), which is determined by calculating the rate of change of the hypervolume index (HV) of two consecutive archive generations: (18); In formula (18), is the hypervolume index of the archive of generation t; is the hypervolume index of the archive of generation t-1; is the threshold.

[0022] The calculation formula of the hypervolume index (HV) is: (19); In formula (19), is the super volume index; is the two-dimensional area calculation formula; is the fitness value vector of the i-th solution; Archive is the external archive; is the ideal value of objective function 1; is the ideal value of objective function 2; is the first objective function value corresponding to the i-th sand cat; is the second objective function value corresponding to the i-th sand cat; Represents the position vector of the i-th sand cat (individual in the algorithm).

[0023] If the maximum iteration is reached, the loop is exited and the optimal solution is output; otherwise, the process returns to S4.2.

[0024] In S4.4, the two-stage selection of similarity distance is specifically as follows: In the first stage, the corresponding similarity distance (SD) is calculated according to the position of each particle in each iteration and the position of each particle in the external document using the following formulas (20) and (21).

[0025] (20); (twenty one); In the above formula, Represents a vector With vector The Euclidean distance of represents the i-th particle in the population; represents the jth non-dominated solution in the external archive; D represents the dimension of the particle; Q is the number of non-dominated solutions in the external archive; represents the position of the i-th particle at the k-th iteration; represents the position of the kth iteration of the i-th non-dominated solution in the external document; represents the similarity distance of the i-th particle; represents the Euclidean distance between the first non-dominated solution in the external document and the i-th particle; represents the Euclidean distance between the second non-dominated solution in the external document and the i-th particle; represents the Euclidean distance between the Qth non-dominated solution and the i-th particle in the external document.

[0026] The similarity distance uses the Euclidean distance, so it can truly reflect the actual distance between particles in the population and particles in the external archive.

[0027] Then, the average similarity distance (AverageSimilarity Distance, ASD) between the i-th particle and the external archive is calculated according to the following formula (22).

[0028] (twenty two); In formula (22), represents the average similarity distance between the i-th particle and the external archive; Represents the similarity between two vectors; represents the number of non-dominated solutions.

[0029] In the second stage, each particle in the population selects one of the non-dominated solutions selected in the first stage as its own global optimal solution, guiding the optimization of the particles in the population. This method allows each particle to select the optimal solution that suits it, improving the uniformity of the Pareto solution.

[0030] The present invention provides a multi-objective optimization method for a circular wireless charging coil for electric vehicles, and the technical effects are as follows: 1) Step 1 of the present invention constructs an equivalent circuit model of the SS-type resonant compensation topology and derives the output power equation (1) and transmission efficiency equation (6). This precise modeling provides a theoretical basis for subsequent optimization and clarifies the relationship between the coupling coefficient equation (7) and system performance.

[0031] 2) Step 2 of the present invention uses the coupling coefficient (objective function 1) and the comprehensive offset reduction rate (objective function 2) as the optimization target formula (13). The dual-objective design takes into account both efficiency and stability and adapts to the needs of actual charging scenarios.

[0032] 3) Step 3 of the present invention determines the coil design variables (number of turns, wire diameter, etc.) and the constraint equation (14), which complies with the national standard GB / T38775.6-2021. The feasibility of the solution is ensured by combining the actual engineering limitations.

[0033] 4) Step 4 of the present invention uses an improved multi-objective sand cat swarm algorithm to select the global optimal solution through two stages of similarity distance, thereby avoiding local optimality, improving the uniformity of the Pareto front, and making the optimization results more reasonable.

[0034] 5) This invention provides a multi-objective optimization method for circular wireless charging coils for electric vehicles. It improves the multi-objective Sand Cat Swarm algorithm, avoids falling into local optimality, and improves the optimization effect. The designed circular wireless charging coil can effectively improve the stability of wireless charging for electric vehicles. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The present invention will be further described below with reference to the accompanying drawings and examples: Figure 1 This is the equivalent circuit model of the SS type resonant compensation topology structure in the present invention.

[0036] Figure 2 This is the optimization flow chart of the multi-objective sand cat swarm algorithm in the present invention.

[0037] Figure 3 This is the multi-objective optimization result of the circular coil in this invention.

[0038] Figure 4 Graphs showing the lateral offset characteristics of the three circular coil structures of the present invention.

[0039] Figure 5 Graphs showing the longitudinal offset characteristics of the three circular coil structures of the present invention.

[0040] Figure 6 Schematic diagram of the circular wireless charging coil model. DETAILED DESCRIPTION

[0041] A multi-objective optimization method for a circular wireless charging coil of an electric vehicle comprises: constructing an equivalent circuit model of an SS-type resonant compensation topology structure of a wireless power transmission system, performing AC impedance analysis on the system, and deriving expressions for system output power and transmission efficiency; determining optimization objectives and parameter optimization objective functions based on the derived expressions for system output power and transmission efficiency; building a circular coil model and determining coil design variables to be optimized; determining constraint conditions according to national standards; and optimizing parameters using an improved multi-objective sand cat swarm optimization algorithm to ultimately obtain optimal parameters for a compensation circuit of the wireless power transmission system. The improved multi-objective sand cat swarm optimization algorithm adopted in the present invention is applied to the optimal design of circular wireless charging coils for electric vehicles, solving the problem that traditional sand cat swarm algorithms are prone to falling into local optimality, resulting in a more reasonable global optimality and better performance of the optimized coils.

[0042] like Figure 1 As shown in the figure, the equivalent circuit model of the SS type resonant compensation topology structure of the wireless power transmission system specifically includes: the primary side is the high-frequency AC power output by the inverter , compensation capacitor , primary coil self-inductance , primary equivalent resistance Series structure; the secondary side is composed of the secondary coil self-inductance , compensation capacitor , load equivalent resistance , secondary side equivalent resistance Series structure; the mutual inductance between the primary coil and the secondary coil is ; The current flowing through the primary and secondary sides is 、 .

[0043] like Figure 2 As shown in FIG, the improved multi-objective sand cat swarm algorithm is used to optimize the parameters, including the following steps: Step 1: Initialize the population, including the number of sand cats and the maximum number of iterations and the position of each sand cat Pos(i); Step 2: Calculate and store the fitness value corresponding to each sand cat position, where the position of the sand cat with the largest fitness value is the current optimal sand cat position. ; Step 3: Determine the fitness value of each sand cat position, perform Pareto sorting, and update the external archive; Step 4: Use similarity distance in two stages to select the global optimal solution in the external archive; Step 5: Determine whether the algorithm meets the termination condition. If the maximum iteration is reached, exit the loop and output the optimal solution; otherwise, return to step 2.

[0044] The two-stage selection of similarity distance in step 4 is as follows: In the first stage, the corresponding similarity distance (SD) is calculated based on the position of each particle in each iteration and the position of each particle in the external document using the following two formulas.

[0045] ; ; Where, represents the i-th particle in the population, represents the jth non-dominated solution in the external archive, D represents the particle dimension, and Q represents the number of non-dominated solutions in the external archive. Similarity distance uses Euclidean distance, which accurately reflects the actual distance between particles in the population and particles in the external archive. The average similarity distance (ASD) between the i-th particle and the external archive is then calculated using the following formula.

[0046] ; In the second stage, each particle in the population selects one of the non-dominated solutions selected in the first stage as its own global optimal solution, guiding the optimization of the particles in the population. This method allows each particle to select the optimal solution that suits it, improving the uniformity of the Pareto solution.

[0047] Set the maximum number of iterations T=100; the external archive size is 100, and 950 sample points are obtained by finite element simulation, with 700 sample points as the training set and 250 sample points as the test set. The optimization results are as follows Figure 3 As shown. Take out 3 special points from the Pareto frontier obtained from the optimization results, Figure 3 The points indicated by the red asterisks. Point A is the point where the coupling coefficient is maximized when facing the target, that is, the transmission efficiency is maximized when facing the target. It is more suitable for situations where offset distance is not easy to occur, such as: a device that fixes the vehicle position at the charging station to avoid offset caused by random parking. Point C is the point where anti-offset performance is maximized and is more suitable for situations where offset is likely to occur. For example, the parking range at the charging station is large and the vehicle position cannot be fixed. Point B is the point closest to the ideal point. The coil structure corresponding to point B has relatively balanced two targets and is also the comparison point for the circular coil in the subsequent comparison with the other two coil structures.

[0048] Finite element simulation shows that the coupling coefficient variation curves of the three circular coil structures are as follows: Figure 4 、 Figure 5 As shown. Figure 4 、 Figure 5 It can be seen that the coupling coefficient of the circular coil optimized by the method of the present invention changes relatively smoothly within the range of 0-100 mm in the horizontal offset and 0-70 mm in the longitudinal offset, and the overall coupling coefficient is at a relatively high level.

Claims

1. A multi-objective optimization method for circular wireless charging coils for electric vehicles, characterized in that The following steps are involved: Step 1: Construct an equivalent circuit model of the SS-type resonant compensation topology structure of the wireless power transmission system, perform AC impedance analysis on it, and obtain the expressions of system output power and transmission efficiency; Step 2: Determine the optimization target based on the derived system output power and transmission efficiency expressions; Step 3: Build a circular wireless charging coil model, determine the wireless charging coil design variables that need to be optimized, and determine the constraints; Step 4: Use the improved multi-objective sand cat swarm algorithm to perform parameter optimization and obtain the optimal design parameters of the wireless charging coil of the wireless power transmission system.

2. The multi-objective optimization method for a circular wireless charging coil for an electric vehicle according to claim 1, characterized in that: In the step 1, constructing an equivalent circuit model of the SS-type resonant compensation topology structure of the wireless power transmission system specifically includes: The primary side is the high-frequency AC power output by the inverter , compensation capacitor , primary coil self-inductance , primary equivalent resistance Series structure; The secondary side is caused by the self-inductance of the secondary coil , compensation capacitor , load equivalent resistance , secondary side equivalent resistance Series structure; The mutual inductance between the primary coil and the secondary coil is ; The currents flowing through the primary and secondary sides are 、 .

3. The multi-objective optimization method for a circular wireless charging coil for an electric vehicle according to claim 2, characterized in that: The system output power expression is: （1）； In formula (1), is the output power, is the system resonant angular frequency; Assume that the coupling coefficient between the primary and secondary coils is , then the self-inductance and mutual inductance of the primary and secondary sides satisfy the expression: （2）； Then the system output power expression is transformed into: （3）； Quality factor of primary and secondary coils 、 The expression is: （4）； （5）； Then the system transmission efficiency satisfies: （6）； In formula (6), Indicates the system transmission efficiency, is the input power; From the expression of output power and transmission efficiency, it can be seen that increasing the system coupling coefficient can improve power and efficiency, so the coupling coefficient is As the first optimization goal, Satisfies the formula: （7）； Where, is the coupling coefficient, is the mutual inductance of the primary and secondary coils, is the self-inductance of the primary coil, is the self-inductance of the secondary coil; In order to obtain a suitable Pareto frontier, the objective function is inversely expressed as: （8）。 4. The multi-objective optimization method for a circular wireless charging coil for an electric vehicle according to claim 3, characterized in that: The offset drop rate in different directions is defined to measure the system's anti-offset performance. The formula is as follows: （9）； （10）； （11）； In the above formula, is the x-direction offset drop rate; is the y-direction offset decrease rate; is the rate of decrease of the offset in the z direction; is the coupling coefficient when the coils are facing each other; is the x-direction offset rate; is the y-direction offset rate; is the z-direction offset rate; Since the wireless charging coil is a symmetrical coil and the electric vehicle is affected by the x and y direction offset when charging, the second optimization goal of the wireless charging coil structure is set as the comprehensive offset reduction rate, which is expressed as follows: （12）； In formula (12), Indicates the comprehensive offset decrease rate.

5. The multi-objective optimization method for a circular wireless charging coil for an electric vehicle according to claim 4, characterized in that: In step 2, two optimization objectives are selected: （13）； In formula (11), is the number of turns of the primary coil, is the primary coil wire diameter, is the primary coil turn spacing, is the number of turns of the secondary coil, is the secondary coil wire diameter, is the secondary coil turn spacing; represents the objective function 1, Represents the objective function 2.

6. The multi-objective optimization method for a circular wireless charging coil for an electric vehicle according to claim 5, characterized in that: In step 3, a circular wireless charging coil model is built to determine the number of turns of the primary coil. , Primary coil wire diameter , primary coil turn spacing , secondary coil turns , secondary coil wire diameter , secondary coil turn spacing is the design variable to be optimized.

7. The multi-objective optimization method for a circular wireless charging coil for an electric vehicle according to claim 6, characterized in that: The coil size satisfies the following requirements: the inner diameter is not less than the sum of the wire diameter and the turn spacing. The size constraints are: （14）； In formula (14), It is expressed as the difference between the inner diameter of the primary coil and the wire diameter and the turn spacing; It is expressed as the difference between the inner diameter of the secondary coil and the wire diameter and the turn spacing; is the radius of the primary coil; is the radius of the secondary coil; Indicates the inner diameter of the primary coil; Indicates the inner diameter of the secondary coil.

8. The multi-objective optimization method for a circular wireless charging coil for an electric vehicle according to claim 7, characterized in that: In step 4, the improved multi-objective sand cat swarm algorithm is as follows: in the original multi-objective sand cat swarm algorithm, the global optimal solution is selected according to the two-stage similarity distance, and the particles in the population are guided to seek the optimal solution to improve the uniformity of the Pareto solution; the improved multi-objective sand cat swarm algorithm includes the following steps: S4.1: Initialize the population, including the number of sand cats N and the maximum number of iterations And the position of each sand cat Pos(i), the formula satisfies: （15）； In formula (15), L is the lower bound of the search space, which is a D-dimensional vector; U is the lower bound of the search space, which is a D-dimensional vector; is a D-dimensional random vector with each component uniformly distributed between [0,1]; S4.2: Calculate and store the fitness value corresponding to each sand cat's position, where the fitness value satisfies: （16）； In formula (16), is the fitness value of the i-th sand cat, which is an M-dimensional vector; M is the number of objective functions; Among them, the position of the sand cat with the largest fitness value is the current optimal sand cat position , optimal sand cat position Satisfies the formula: （17）； In formula (17), arg min is the instruction that returns the position that minimizes the function value; Archive is the external archive; S4.3: Determine the fitness value of each sand cat position and perform Pareto sorting. The specific logic is: S4.3.1: Traverse all sand cat locations in the population and compare dominance relationships between them; S4.3.2: Classify non-dominated hierarchies according to dominance relationships: Rank 1: Individuals that are not dominated by any solution; Rank 2: individuals dominated only by Rank 1 individuals, and so on; S4.3.3: Store all Rank 1 individuals in an external archive; S4.4: Use similarity distance in two stages to select the global optimal solution in the external archive; S4.5: Determine whether the algorithm meets the termination conditions.

9. The multi-objective optimization method for a circular wireless charging coil for an electric vehicle according to claim 8, characterized in that: In S4.4, the two-stage selection of similarity distance is specifically as follows: In the first stage, the similarity distance (SD) is calculated based on the position of each particle in each iteration and the position of each particle in the external document using the following equations (20) and (21). （20）； （21）； In the above formula, Represents a vector With vector The Euclidean distance of represents the i-th particle in the population; represents the jth non-dominated solution in the external archive; D represents the dimension of the particle; Q is the number of non-dominated solutions in the external archive; represents the position of the i-th particle at the k-th iteration; represents the position of the kth iteration of the i-th non-dominated solution in the external document; represents the similarity distance of the i-th particle; represents the Euclidean distance between the first non-dominated solution in the external document and the i-th particle; represents the Euclidean distance between the second non-dominated solution in the external document and the i-th particle; represents the Euclidean distance between the Qth non-dominated solution and the i-th particle in the external document; The similarity distance uses the Euclidean distance, so it can truly reflect the actual distance between particles in the population and particles in the external archive; Then, the average similarity distance (AverageSimilarity Distance, ASD) between the i-th particle and the external archive is calculated according to the following formula (22); （22）； In formula (22), represents the average similarity distance between the i-th particle and the external archive; Represents the similarity between two vectors; represents the number of non-dominated solutions; In the second stage, one of the non-dominated solutions selected in the first stage is selected for each particle in the population as its own global optimal solution, guiding the optimization of the particles in the population.

10. The multi-objective optimization method for a circular wireless charging coil for an electric vehicle according to claim 8, characterized in that: In S4.5, the algorithm is judged to meet the termination condition as follows: The Pareto front converges and the improvement of the solution set is lower than the threshold. This is determined by calculating the change rate of the hypervolume index (HV) of two adjacent generations of archives: （18）； In formula (18), is the hypervolume index of the archive of generation t; is the hypervolume index of the archive of generation t-1; is the threshold; The calculation formula of the hypervolume index HV is: （19）； In formula (19), is the super volume index; is the two-dimensional area calculation formula; is the fitness value vector of the i-th solution; Archive is the external archive; is the ideal value of objective function 1; is the ideal value of objective function 2; is the first objective function value corresponding to the i-th sand cat; is the second objective function value corresponding to the i-th sand cat; represents the position vector of the i-th sand cat individual; If the maximum iteration is reached, the loop is exited and the optimal solution is output; otherwise, the process returns to S4.2.

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