Multi-objective optimization design method for wireless charging system

Abstract

The invention discloses a multi-objective optimization design method of a wireless charging system, which realizes collaborative optimization of multiple objectives by introducing K-means clustering and non-dominated sorting to a particle swarm algorithm, and realizes that individuals are concentrated on an intersection of a preference area and a Pareto frontier by adding sorting and screening based on the preference area, thereby improving the optimization efficiency of the wireless charging system. And the individual density is improved on the premise of ensuring the individual dispersity. Therefore, by adopting the design method provided by the invention, multiple targets can be optimized, and meanwhile, a decision maker is allowed to specify a preference interval and guide individuals to gather towards the interval. Compared with other similar algorithms, the method has the advantages of being small in calculation amount, good in dispersity and capable of achieving multi-objective optimization with preference.

Description

Technical Field

[0001] The present invention belongs to the technical field of power electronics design, and particularly relates to a multi-objective optimization design method for a wireless charging system. Background Art

[0002] With the rapid development of technology, wireless charging technology has become a major innovation highlight in the field of electronic device charging. Compared with the traditional wired charging method, wireless charging has won wide attention and application due to its convenience, flexibility, and friendliness to device interfaces. From smartphones, tablets to electric vehicles, wireless charging technology is gradually penetrating into all aspects of our lives, bringing users an unprecedented charging experience.

[0003] In the existing technologies of wireless charging systems, researchers have been continuously exploring and optimizing the energy transfer mechanism, aiming to improve the charging efficiency, expand the charging range, and enhance the stability of the system. As one of the current mainstream technologies, electromagnetic induction wireless charging realizes the wireless transmission of electrical energy through the principle of electromagnetic induction between the primary coil and the secondary coil. However, there are many technical challenges involved in this process, such as magnetic field coupling efficiency, energy loss, electromagnetic interference, and the impact of the device placement position on the charging efficiency, etc.

[0004] To solve these technical problems, as the core component in the wireless charging system, the parameter design of the magnetic coupler is particularly important. The parameters of the magnetic coupler include but are not limited to the number of turns of the coil, the shape of the coil, the core material and its size, etc., all of which have a profound impact on the performance of the wireless charging system. Reasonable parameter design can significantly improve the magnetic field coupling efficiency, reduce energy loss, and at the same time reduce electromagnetic interference, ensuring the stability and safety of the wireless charging system.

[0005] The parameters of the magnetic coupler should be optimized to meet the actual requirements. Usually, there are multiple optimization objectives. Therefore, in this case, multi-objective optimization is necessary. Rule-based multi-objective optimization is a method for optimizing the coupler, such as in the literature [H.R. Cha, K.R. Park, T.J. Kim and R.Y. Kim, "Design of Magnetic Structure for Omnidirectional Wireless Power Transfer" IEEE Trans. Power Electron. vol. 36, no. 8, pp. 8849-8860, Aug. 2021]. It uses manually set rules or mathematical models to determine the optimization direction. However, it may be difficult to set the optimization rules and requires rich experience. Multi-objective optimization methods based on non-dominated sorting, such as the non-dominated sorting genetic algorithm II (NSGA-II) and the literature [J. Ma, Z. Li, Y. Liu, M. Ban, and W. Song, "Thermal Analysis and Optimization of the Magnetic Coupler for Wireless Charging System" IEEE Trans. Power Electron. vol. 38, no. 12, pp. 16269-16280, Dec. 2023], are widely used in the multi-objective optimization of wireless charging systems. These algorithms select elite individuals through non-dominated sorting and then perform crossover and mutation operations to enhance individual diversity and achieve a good distribution on the Pareto front. However, their convergence and stability are relatively poor. Multi-objective hybrid particle swarm optimization (MOHPSO) is also used to optimize the design of wireless charging magnetic couplers. Usually, such methods evenly distribute individuals throughout the Pareto front, including some extreme individuals. However, decision-makers usually prefer more balanced individuals. Summary of the Invention

[0006] In view of the above, the present invention provides a multi-objective optimization design method for a wireless charging system to optimize the design parameters of the wireless charging system so that it can meet the needs of decision-makers.

[0007] A multi-objective optimization design method for a wireless charging system includes the following steps:

[0008] (1) Determine the optimization objectives, preference regions, parameters to be optimized and their value ranges of the magnetic coupler in the wireless charging system according to the actual requirements;

[0009] (2) Determine the relevant parameters of the particle swarm algorithm according to the actual requirements;

[0010] (3) Establish the initial population of the particle swarm optimization algorithm. Each individual in the population corresponds to a set of numerical combinations of all the parameters to be optimized for the magnetic coupler.

[0011] (4) Calculate the fitness of each individual (composed of the specific values of each optimization objective) through simulation, and update the historical best particle of each individual according to the fitness.

[0012] (5) Divide all individuals into multiple clusters according to the fitness using the K-means clustering algorithm.

[0013] (6) Perform non-dominated sorting on the individuals within each cluster according to the fitness, and select the individuals at the first level as the candidate particles for each cluster.

[0014] (7) Select the leader particle of each cluster and the global best particle of the population from the candidate particles.

[0015] (8) Update each individual according to the leader particle and the global best particle.

[0016] (9) Determine whether the maximum number of iterations has been reached: If so, stop the particle swarm optimization algorithm and output the leader particle of each current cluster and the global best particle for the user to select one particle as the design scheme of the magnetic coupler; otherwise, update the inertia coefficient and the following coefficient, increment the number of iterations by 1, and then return to execute step (4).

[0017] The wireless charging system consists of an inverter, a transmitter-side compensation circuit, a magnetic coupler, a receiver-side compensation circuit, and a rectifier bridge. The magnetic coupler includes a transmitting coil and a receiving coil. The transmitting coil is cascaded with the transmitter-side compensation circuit and is connected to both ends of the AC side of the inverter together. The receiving coil is cascaded with the receiver-side compensation circuit and is connected to both ends of the AC side of the rectifier bridge together. The DC side of the rectifier bridge is connected to the load. The receiving coil is placed directly above the transmitting coil, with a certain distance and a certain degree of offset between them.

[0018] Furthermore, in step (1), various parameters of the magnetic coupler including the number of turns, size, and shape are used as the parameters to be optimized. At the same time, the value ranges of these parameters are determined according to the geometric constraint relationships and actual requirements; meanwhile, the mutual inductance, rate of change of mutual inductance, and self-inductance of the magnetic coupler are used as the optimization objectives, and the value ranges of these optimization objectives are used as the preference regions.

[0019] Furthermore, the relevant parameters of the particle swarm algorithm in step (2) include the number of individuals in the population, the number of clusters, the initial individual, the initial inertia coefficient C0, and the initial following coefficients a0 to c0, wherein the number of individuals in the population is determined according to the actual situation, and considering the convenience of establishing the initial population by the Latin hypercube sampling method, a perfect square number or other numbers that are convenient for constructing an orthogonal table are selected; the number of clusters is 3 to 5, the dimension of the initial individual is the number of parameters to be optimized, and the value of the corresponding dimension is randomly selected in the range of 0 to K, K is 1 / 2 of the middle value of the corresponding parameter value range to be optimized; the initial inertia coefficient C0 is 0.8 to 0.95, the initial following coefficient a0 is 0.7 to 0.9, b0 is 0 to 0.2, and c0 is 0.3 to 0.6.

[0020] Furthermore, in step (3), the Latin Hypercube Sampling (LHS) method is used to establish the initial population of the particle swarm algorithm, that is, for any parameter to be optimized, its value range is evenly divided into multiple level values, and then the corresponding orthogonal table is constructed, a point is randomly selected inside the area corresponding to each level value, and substituted into the level value combination in the orthogonal table, thus completing the Latin hypercube sampling.

[0021] Furthermore, for any individual in step (4), by modeling the magnetic coupler and performing finite element analysis, simulation data of the individual under the corresponding parameter combination including the mutual inductance, mutual inductance change rate and self-inductance of the magnetic coupler are obtained, and these simulation data are preprocessed to obtain the fitness of the individual, that is, the fitness value of each optimization target.

[0022] Furthermore, in step (4), for any individual, a historical optimal particle is stored correspondingly. After the individual is updated and the fitness of the current individual is obtained through simulation calculation, the fitness of the current individual is compared with the fitness of the historical optimal particle. If the current individual dominates the historical optimal particle, the current individual is updated as the historical optimal particle, otherwise the historical optimal particle remains unchanged.

[0023] Furthermore, the criterion for non-dominated sorting of individuals in the cluster in step (6) is: for any two individuals A and B, if the following conditions are met, then individual A is considered to dominate individual B, and A is at a higher level;

[0024]

[0025] Among them: A i and B i are the fitness values ​​of individuals A and B with respect to the optimization target i, i is the index number of the optimization target, and Φ represents the set of optimization targets; if an individual is not dominated by any individual, it is at the highest level, and the rest of the individuals are similar, and so on, and all individuals can be sorted by non-domination.

[0026] Further, the specific implementation of step (7) is as follows: for any cluster, filter out the particles with fitness within the preference region from the candidate particles, and randomly select one particle from the filtered particles as the leader particle of the cluster; if none can be filtered out, calculate the Euclidean distance between the fitness of each candidate particle and the center of the preference region, and select the candidate particle with the closest distance as the leader particle of the cluster; for the population, first perform non-dominated sorting on all individuals, and then find the leader particle in the way described above from the individuals in the first level. This leader particle is the global optimal particle of the population.

[0027] Further, for any individual i in step (8), it is updated through the following expression:

[0028]

[0029] where: C n-1 is the inertia coefficient of the (n - 1)-th iteration, a n-1 , b n-1 , c n-1 are the following coefficients of the (n - 1)-th iteration, and are individual i of the (n - 1)-th iteration and the n-th iteration respectively (i.e., individual i before and after one update), and are the offsets of individual i of the (n - 1)-th iteration and the n-th iteration respectively, is the leader particle of the cluster to which individual i belongs in the (n - 1)-th iteration, is the global optimal particle of the (n - 1)-th iteration, is the historical optimal particle of individual i in the (n - 1)-th iteration, i is the individual index number, and n is the iteration round index number.

[0030] Further, in step (9), the inertia coefficient and the following coefficients are updated through the following expressions:

[0031]

[0032] where: X n and X n-1 are the inertia coefficient or the following coefficients of the n-th iteration and the (n - 1)-th iteration respectively, i.e., X = C, a, b, c, N max is the maximum number of iterations, and X0 is the initial inertia coefficient or the initial following coefficient.

[0033] The multi-objective optimization design method of the wireless charging system of the present invention realizes the collaborative optimization of multiple objectives by introducing K-means clustering and non-dominated sorting into the particle swarm algorithm, and adds sorting and screening based on the preference region, so that individuals are concentrated in the intersection of the preference region and the Pareto front, and the individual density is improved while ensuring the dispersion of individuals.

[0034] Therefore, the design method of the present invention can optimize multiple objectives and at the same time allow the decision maker to specify a preference interval to guide individuals to gather in this interval. Compared with other similar algorithms, the method of the present invention has the advantages of less computational complexity, better dispersion, and can achieve multi-objective optimization with preferences. Brief Description of the Drawings

[0035] Figure 1 It is a schematic flow chart of the particle swarm algorithm in the present invention.

[0036] Figure 2 It is a schematic structural diagram of the magnetic coupler coil of a nested structure in the embodiment of the present invention.

[0037] Figure 3 It is a schematic diagram of the mutual inductance performance of the magnetic coupler under the parameter optimization scheme of the present invention. Detailed Description of the Invention

[0038] In order to describe the present invention more specifically, the technical solutions of the present invention will be described in detail below in conjunction with the drawings and specific embodiments.

[0039] The multi-objective optimization design method of the wireless charging system of the present invention is based on the widely used particle swarm optimization algorithm. Each parameter combination is regarded as a particle moving in the feasible region, and the fitness of the particle is regarded as its coordinates. The velocity of the particle consists of several parts, including the inertial velocity, the velocity towards the global optimum, and the velocity towards the historical optimum. As the algorithm progresses, the inertial coefficient of the particle becomes smaller and finally approaches the global optimum value.

[0040] However, the particle swarm optimization algorithm may encounter difficulties when applied to multi-objective optimization. Although randomness can be introduced in the selection process, a single global optimum value may still lead to poor particle dispersion. Therefore, the present invention uses the K-means method to divide the particle swarm into several parts to improve the dispersion of the optimization method. When using the k-means method to divide the particle swarm, the first step is to randomly select the center points of each cluster; next, the cluster where each particle is located is determined by the principle of proximity, and the center point of the particles in each cluster is calculated. The method for calculating the center point is shown in the following formula:

[0041]

[0042] Among them: Center(i) refers to the value of the i-th dimension of the cluster center point, p j (i) represents the i-th dimension value of the j-th particle in the cluster.

[0043] After updating the center point of each cluster using the above formula, each particle is reclassified based on the proximity principle; then, the above process is repeated until the number of operations is reached or the particle classification does not change. When there are no particles in the cluster in some cases, their center point will be replaced by the average of the centers of other clusters and a random number will be added.

[0044] After that, the particles in each cluster are sorted by non-domination, and the particles in each cluster that are not dominated by other particles are selected as candidate particles; the definition of "dominance" here is:

[0045]

[0046] Where: a and b refer to two particles, ai and bi refer to their i-th function values. If for any function value, ai≤bi, then particle a dominates particle b.

[0047] Next, determine whether the candidate particle is in the preferred region: if so, randomly select a candidate particle in the preferred region as the leader particle of the cluster; otherwise, select the candidate particle closest to the center of the preferred region as the leader particle of the cluster. At the same time, perform a non-dominated sort on all particles and select a global leader particle according to the above principle.

[0048] Finally, the speed of each particle is determined. The speed of each particle is composed of four parts, as shown in the following formula: inertial speed, speed toward the leader particle of its cluster, speed toward the global leader particle, and speed toward the historical optimum.

[0049] V in =Ci*V i(n-1) +a*(P cb -P i )+b*(P gb -P i )+c*(P hb -P i )

[0050] Where: Ci is the inertia coefficient, abc is the predetermined following coefficient, P cb is the leader particle of the cluster to which the particle belongs, P gb is the global optimal particle, P hb is the historical optimal individual of the particle.

[0051] like Figure 1 As shown in Figure 2, the process of the particle swarm algorithm is as follows:

[0052] (1) Initialize all algorithm parameters, including the maximum number of iterations, the number of clusters, the initial velocity, etc.;

[0053] (2) Define the preferred region and calculate the center point;

[0054] (3) Use LHS to generate the initial particle swarm;

[0055] (4) Use finite element analysis software to analyze the performance of the particles and calculate their fitness according to the simulation results;

[0056] (5) Divide the particles into clusters based on the K-means method;

[0057] (6) Use non-dominated sorting to sort each particle cluster and select candidate particles;

[0058] (7) Select the leading particle of each cluster and the global optimal particle;

[0059] (8) Calculate the velocity of each particle and update the parameters of each particle;

[0060] (9) Determine whether the stopping condition is satisfied: if the stopping condition is satisfied, stop the algorithm and output the result; otherwise, increment the number of iterations by 1 and then return to step (4).

[0061] Embodiment

[0062] There is a coil with a nested structure that needs to be optimized. The coil structure is as Figure 2 shown, where the orange part (inner coil) is the transmitting coil and the blue part (outer coil) is the receiving coil. During actual operation, the receiving coil may rotate and move up and down. The number of turns of the two coils of the receiving coil is equal, the number of turns of the two outer coils of the transmitting coil is equal, and the number of turns of the middle coil is arbitrary. Therefore, the parameters to be optimized are: the number of turns NT1 of the middle coil of the transmitting coil, the number of turns NT2 of the outer coil at the transmitting end, the number of turns NR of the receiving coil (the value ranges of all three are 1 to 18 turns) and the total length LR of the receiving coil, with a value range of 50 to 100 mm and a step size of 5 mm. According to the above value range, there are 18 * 18 * 18 * 11 = 64152 possible parameter combinations, and it is obviously impossible to screen the most suitable combination by the exhaustive method. At the same time, according to the circuit calculation results, the self-inductance of the transmitting end of the coupler should not be greater than 40 uH and as small as possible, the mutual inductance must be around 15 uH, the coupling coefficient is around 0.35 and it should have as good an anti-longitudinal offset ability as possible. Therefore, the optimization objective can be defined by the following formula:

[0063]

[0064] G2 = L1 / 40 + |(k - 0.35) / 0.35|

[0065] Where: ΔM represents the percentage change in the mutual inductance of the coupler within a predetermined offset range (±70 mm), M0 represents the mutual inductance of the coupler without offset, L1 represents the self-inductance of the transmitting-end coil of the coupler, and k is the coupling coefficient of the coupler; G1 and G2 are two values of fitness (i.e., two optimized target values), the preference interval of G1 is within 0.2, and the preference interval of G2 is 0.3 - 0.8.

[0066] When using the optimization algorithm, each parameter combination (NT1, NT2, NR, and LR) is regarded as an individual, and its fitness value is obtained through calculation based on the self-inductance and mutual inductance obtained by simulating with ANSYS maxwell software. The specific steps are as follows:

[0067] First, initialize the algorithm parameters. In this embodiment, the number of population individuals is set to 36, the maximum number of iterations is set to 25, the number of clusters is 5, the initial velocity of an individual is an array containing 4 elements, the first three elements are random numbers between 0 and 9, and the last one is a random number between 0 and 25. The initial inertia coefficient of an individual is 0.9, which linearly decreases with the increase of the number of iterations and decreases to the end value of 0.4 at the last iteration (the 25th time); the following coefficients are taken as: a linearly decreases from 0.8 to 0.2, b = 0.1, and c linearly decreases from 0.5 to 0.1.

[0068] Then, use Latin hypercube sampling to select the initial population. The initial population generated in this way is shown in Table 1:

[0069] Table 1

[0070] Serial number LR NT1 NT2 NR Serial number LR NT1 NT2 NR 1 80 14 1 6 19 90 17 10 2 2 100 12 2 9 20 70 3 10 17 3 80 4 2 13 21 90 8 11 12 4 100 3 2 16 22 110 4 11 13 5 60 17 3 3 23 110 15 12 6 6 60 9 3 12 24 70 10 12 8 7 110 5 4 1 25 100 3 13 6 8 70 3 4 4 26 80 4 14 1 9 90 17 4 8 27 100 10 14 15 10 110 13 5 11 28 60 9 14 18 11 70 11 5 13 29 60 16 15 9 12 90 8 6 18 30 80 15 15 10 13 100 11 7 3 31 70 11 16 1 14 60 7 7 6 32 110 5 16 8 15 100 2 7 11 33 90 18 16 13 16 60 17 8 14 34 90 7 17 5 17 80 5 9 9 35 70 2 18 12 18 80 14 9 16 36 110 15 18 18

[0071] Then, simulate the above 36 parameter combinations and calculate the two fitness values of each individual.

[0072] Next, divide these individuals into 5 clusters according to the K-means clustering algorithm, find the leading particle that each particle should follow according to steps (6) and (7), and update each particle according to step (8). At this time, if the parameters of a particle do not meet the requirements, they shall be processed according to the following method: If non-integers appear in N1, N2, and NR, they shall be rounded according to the rounding principle. If the rounded value is less than 1 or greater than 18, it shall be replaced with the closest boundary value; if LR is not a multiple of 5, it shall be replaced with the nearest multiple of 5. If the replaced value is not within the range, it shall be replaced with the closest boundary value.

[0073] Finally, simulate the updated individuals, calculate the fitness, and perform the next iteration; if the number of iterations has reached the maximum, stop the iteration and output the result. After 25 iterations, some of the final results output by the algorithm are shown in Table 2:

[0074] Table 2

[0075]

[0076] As can be seen from the above table, these results are all within the preferred range; according to the actual requirements, the individuals in the 3rd group (in bold) were selected for further experiments, and the mutual inductance performance of this parameter combination is as Figure 3 shown: when the receiver rotates, the mutual inductance does not change; in addition, the mutual inductance of the coupler can maintain a fluctuation of no more than 6% within the offset range of ±70 mm, as shown by the thick black line frame in the figure, which exceeds 45% of the length of the transmitter coil, achieving good performance.

[0077] The above description of the embodiments is to enable those of ordinary skill in the art to understand and apply the present invention. It is obvious that those who are familiar with the technology in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative labor. Therefore, the present invention is not limited to the above embodiments, and all improvements and modifications made by those skilled in the art based on the disclosure of the present invention should be within the protection scope of the present invention.

Claims

1. A multi-objective optimization design method for a wireless charging system, comprising the following steps: (1) Determine the optimization target, preferred area, parameters to be optimized and their value range of the magnetic coupler in the wireless charging system according to actual needs; (2) Determine the relevant parameters of the particle swarm algorithm according to actual needs; (3) Establishing the initial population of the particle swarm algorithm, each individual in the population corresponds to a set of numerical combinations of all parameters to be optimized of the magnetic coupler; (4) Calculate the fitness of each individual through simulation, and update the historical optimal particle of each individual according to the fitness; (5) Using K-means clustering algorithm to divide all individuals into multiple clusters according to fitness; (6) Perform non-dominated sorting on the individuals in each cluster according to their fitness, and select the individuals at the first level as candidate particles for each cluster; (7) Select the leader particle of each cluster and the global optimal particle of the population from the candidate particles; (8) Update each individual according to the leader particle and the global optimal particle; (9) Determine whether the maximum number of iterations has been reached: If so, stop the particle swarm algorithm and output the leader particle of each cluster and the global optimal particle for the user to select a particle as the design scheme of the magnetic coupler; otherwise, update the inertia coefficient and the following coefficient, increase the number of iterations by 1, and then return to step (4).

2. The multi-objective optimization design method of the wireless charging system according to claim 1, characterized in that: In the step (1), various parameters of the magnetic coupler including the number of turns, size, and shape are used as parameters to be optimized, and the value ranges of these parameters are determined according to geometric constraints and actual needs; at the same time, the mutual inductance, mutual inductance change rate, and self-inductance of the magnetic coupler are used as optimization targets, and the value ranges of these optimization targets are used as preferred areas.

3. The multi-objective optimization design method of the wireless charging system according to claim 1, characterized in that: The relevant parameters of the particle swarm algorithm in step (2) include the number of individuals in the population, the number of clusters, the initial individual, the initial inertia coefficient C0, and the initial following coefficients a0-c0, wherein the number of individuals in the population is determined according to the actual situation, and the Latin hypercube sampling method is considered to facilitate the establishment of the initial population, and the perfect square number or other numbers that are convenient for constructing an orthogonal table are selected; The number of clusters is 3 to 5, the dimension of the initial individual is the number of parameters to be optimized, and the value of the corresponding dimension is randomly selected in the range of 0 to K, where K is 1 / 2 of the middle value of the corresponding parameter value range to be optimized; the initial inertia coefficient C0 is 0.8 to 0.95, the initial following coefficient a0 is 0.7 to 0.9, b0 is 0 to 0.2, and c0 is 0.3 to 0.

6.

4. The multi-objective optimization design method of the wireless charging system according to claim 1, characterized in that: In step (3), the Latin hypercube sampling method is used to establish the initial population of the particle swarm algorithm, that is, for any parameter to be optimized, its value range is evenly divided into multiple level values, and then the corresponding orthogonal table is constructed, a point is randomly selected from the area corresponding to each level value, and substituted into the level value combination in the orthogonal table, thus completing the Latin hypercube sampling.

5. The multi-objective optimization design method of the wireless charging system according to claim 1, characterized in that: In the step (4), for any individual, by modeling the magnetic coupler and performing finite element analysis, simulation data of the individual corresponding to the parameter combination is obtained, including the mutual inductance, mutual inductance change rate and self-inductance of the magnetic coupler, and these simulation data are preprocessed to obtain the fitness of the individual, that is, the fitness value of each optimization target.

6. The multi-objective optimization design method of the wireless charging system according to claim 1, characterized in that: In the step (4), for any individual, a historical optimal particle is stored correspondingly. After the individual is updated and the fitness of the current individual is obtained through simulation calculation, the fitness of the current individual is compared with the fitness of the historical optimal particle. If the current individual dominates the historical optimal particle, the current individual is updated as the historical optimal particle, otherwise the historical optimal particle remains unchanged.

7. The multi-objective optimization design method of the wireless charging system according to claim 1, characterized in that: The standard for non-dominated sorting of individuals in the cluster in step (6) is: for any two individuals A and B, if the following conditions are met, it is considered that individual A dominates individual B, and A is at a higher level; Among them: A i and B i are the fitness values ​​of individuals A and B with respect to the optimization target i, i is the index number of the optimization target, and Φ represents the set of optimization targets; if an individual is not dominated by any individual, it is at the highest level, and the rest of the individuals are similar, and so on, and all individuals can be sorted by non-domination.

8. The multi-objective optimization design method for a wireless charging system according to claim 1, characterized in that: The specific implementation method of step (7) is as follows: for any cluster, particles whose fitness is within the preferred region are screened from the candidate particles, and a particle is randomly selected from the screened particles as the leader particle of the cluster; if none can be screened out, the Euclidean distance between the fitness of each candidate particle and the center of the preferred region is calculated, and the candidate particle with the closest distance is selected as the leader particle of the cluster; for the population, all individuals are first non-dominated sorted, and then the leader particle is searched from the individuals of the first level in the above manner, and the leader particle is the global optimal particle of the population.

9. The multi-objective optimization design method of the wireless charging system according to claim 1, characterized in that: In step (8), for any individual i, it is updated by the following expression: Where: C n-1 is the inertia coefficient of the n-1th iteration, a n-1 , b n-1 、c n-1 is the following coefficient of the n-1th iteration, and are the individual i of the n-1th iteration and the nth iteration respectively (i.e., individual i before and after an update), and are the offsets of individual i in the n-1th iteration and the nth iteration, respectively. is the leader particle of the cluster to which individual i belongs in the n-1th iteration, is the global optimal particle of the n-1th iteration, is the historical optimal particle of individual i in the n-1th iteration, i is the individual index number, and n is the iteration round index number.

10. The multi-objective optimization design method for a wireless charging system according to claim 9, characterized in that: In step (9), the inertia coefficient and the following coefficient are updated by the following expressions: Where: X n and X n-1 are the inertia coefficients or follow-up coefficients of the nth iteration and the n-1th iteration, that is, X = C, a, b, c, N max is the maximum number of iterations, and X0 is the initial inertia coefficient or initial following coefficient.

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