An improved four-vector optimization algorithm-based mcr-wpt system planar coil structure parameter optimization method

Abstract

The application provides an MCR-WPT system plane coil structure parameter optimization method based on an improved four-vector optimization algorithm; an S-S topology compensation structure network is analyzed, and the energy transmission efficiency of the MCR-WPT system is derived; the influence of the coil physical structure on the coil characteristic parameters is analyzed, and the self-inductance value of the coil is calculated; the mutual inductance coefficient value between the coupled coils is calculated; the alternating current resistance is calculated; the coupling coefficient between the coupled coils is calculated, the frequency splitting is analyzed to establish a constraint condition; the optimization variables are determined, and the energy transmission efficiency is taken as the objective function value and the optimization target; the constraint condition is set according to the critical coupling coefficient, and the parameter range is adjusted according to the constraint condition; and the improved four-vector optimization algorithm is used to optimize the energy transmission efficiency, that is, the objective function, according to the coil setting parameters.

Description

Technical Field

[0001] This application relates to the field of electronic equipment technology, and in particular to a method for optimizing the structural parameters of planar coils in an MCR-WPT system based on an improved four-vector optimization algorithm. Background Technology

[0002] In wireless power transfer (WPT) technology, magnetically coupled resonant (MCR) wireless power transfer systems have received widespread attention and application due to their high efficiency, safety, and long-distance transmission capabilities. However, how to effectively improve the energy transfer efficiency of MCR-WPT systems has become an important research topic. Traditional wireless power transfer systems are prone to energy loss during transmission due to factors such as coil design, frequency selection, and compensation topology, which affects the overall performance of the system.

[0003] To address these issues, researchers have proposed various improvement methods to optimize the performance of the MCR-WPT system, particularly focusing on optimizing the coupling coil structure. The physical structural parameters of the coils, such as wire diameter, pitch, and coil spacing, directly affect the system's resonant frequency, coupling coefficient, and transmission efficiency. Furthermore, the skin effect and proximity effect increase the AC resistance of the coils under high-frequency operating conditions, further leading to energy loss.

[0004] Therefore, the rational design of the coupling coil and the optimization of its structural parameters are crucial for improving the efficiency of wireless power transmission systems. Summary of the Invention

[0005] This application provides a method for optimizing the planar coil structure parameters of the MCR-WPT system based on an improved four-vector optimization algorithm, which can be used to solve the technical problem of power loss in the process of power transmission under high-frequency conditions.

[0006] This application provides a method for optimizing the planar coil structure parameters of an MCR-WPT system based on an improved four-vector optimization algorithm. The method includes:

[0007] Step S1: Analyze the SS topology compensation structure network and derive the energy transfer efficiency of the MCR-WPT system;

[0008] Step S2: Analyze the influence of the coil's physical structure on the coil's characteristic parameters, including: coil self-inductance, mutual inductance, resistance, and coupling coefficient;

[0009] Step S3: Calculate the self-inductance of the coil;

[0010] Step S4: Calculate the mutual inductance coefficient between the coupled coils;

[0011] Step S5: Calculate the AC resistance of the Litz line under high-frequency AC conditions;

[0012] Step S6: Calculate the coupling coefficient between the coupled coils and analyze the frequency splitting to establish constraint conditions;

[0013] Step S6: Determine the optimization variables, using energy transfer efficiency as the objective function value and optimization objective;

[0014] Step S8: Set constraint conditions based on the critical coupling coefficient: k≤k s And adjust the parameter range according to the constraints;

[0015] Step S9: Based on the coil setting parameters, the improved four-vector optimization algorithm is used to optimize the energy transfer efficiency, i.e., the objective function.

[0016] This invention optimizes the parameters of coupled coil structures using an improved four-vector optimization algorithm, achieving faster convergence, higher accuracy, and more stable results compared to the original algorithm. First, an initial population is generated using SPM chaotic mapping, reducing randomness, increasing population diversity, and facilitating rapid convergence to achieve the global optimum. Then, a cross-sectional strategy is used for the first position update. This strategy includes horizontal and vertical cross-sectional ...

[0017] This invention significantly improves the energy transfer efficiency of a magnetically coupled resonant wireless power transfer (MCR-WPT) system by optimizing the planar coil structure parameters, while simplifying the calculation process. First, an SS topology compensation structure is selected as the basis for circuit design, and the system's energy transfer efficiency formula is derived as the objective function for optimization. This formula considers various influencing factors while ensuring the simplicity and accuracy of the calculation, making the optimization process more efficient while keeping the results within the allowable error range. Furthermore, this invention uses Litz wire-wound coupling coils, successfully solving the resistance loss problem caused by the skin effect and proximity effect at high frequencies, further reducing energy loss at high frequencies. This design not only ensures high accuracy of the optimization results but also maintains the simplicity of the calculation process, ensuring that ideal optimization results can be obtained in a short time, meeting the requirements of practical applications. Through multiple iterations, this invention can output the optimal coil physical parameters, enabling the MCR-WPT system to operate in the best coupling state, improving system efficiency and simplifying the calculation process, providing an efficient and easy-to-implement optimization solution for wireless power transfer systems. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the present invention;

[0019] Figure 2 This is a schematic diagram of the SS topology in this invention;

[0020] Figure 3 This is a flowchart of the improved four-vector optimization algorithm in this invention;

[0021] Figure 4 This is a schematic diagram of the transient model of the coupling coil in this invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0023] The embodiments of this application will now be described in conjunction with the accompanying drawings.

[0024] Referring to Figure (1), this invention is a method for optimizing the planar coil structure parameters of an MCR-WPT system based on an improved four-vector optimization algorithm. The method includes the following steps:

[0025] Step S1: Analyze the SS topology compensation network and calculate and derive the energy transfer efficiency formula for the MCR-WPT system;

[0026] The coil structure is optimized by adjusting the wire diameter, screw diameter, spacing, and power supply frequency.

[0027] The optimal parameters of the coil structure are obtained by using an improved four-vector optimization algorithm based on the coupling coil parameters. The energy transfer efficiency formula of the MCR-WPT system, i.e., the objective function, is:

[0028]

[0029] In the formula, η represents the energy transfer efficiency of the system; ω is the resonant angular frequency of the system; M is the mutual inductance of the coupled coils; R1 and R2 represent the internal resistances of the primary and secondary coils, respectively; R L Indicates the system load size;

[0030] Step S2: Analyze the influence of the coil's physical structure on its characteristic parameters; design the parameters of the coupled coil to determine the transmission efficiency, specifically including: coil self-inductance, mutual inductance, resistance, and coupling coefficient.

[0031] Step S3: Calculate the self-inductance of the coil. When current flows through the coil in a closed loop, the change in current causes a corresponding change in the magnetic field around the coil. According to the principle of electromagnetic induction, this change in magnetic field will generate an induced electromotive force in the coil; this phenomenon is called self-inductance.

[0032]

[0033] In the formula: L is the self-inductance, N is the number of turns, μ0 is the free permeability, and r avg Average wire diameter r max r is the outer radius of the coil. min Let C1 = 2.46 and C2 = 0.2 be the inner radius of the coil.

[0034] Step S4: Calculate the mutual inductance coefficient between the coupled coils. When the current in one current-carrying loop changes, this change induces a current in another adjacent loop; this phenomenon is called mutual inductance.

[0035]

[0036] In the formula, M is the mutual inductance, μ0 is the free permeability, and N is the free permeability. r N represents the number of turns of the primary coil. t r is the number of turns of the secondary coil. r r is the average radius of the primary coil. t Let be the average radius of the secondary coil, and h be the distance between the coils.

[0037] Step S5: Calculate the AC resistance of the Litz wire under high-frequency AC conditions. The coil resistance is a major factor affecting the energy transfer efficiency of the MCR-WPT system. Under high-frequency current, the wire is affected by the skin effect and proximity effect. No current flows inside the wire; the current concentrates on the surface, and when the wires are too close together, the current is attracted to the adjacent side, leading to increased resistance. To reduce the losses caused by the increased AC resistance of the coil under high-frequency conditions and improve the energy transfer efficiency of the MCR-WPT system, Litz wire is used when manufacturing the coil. The Litz wire is composed of multiple insulated, relatively thin wires wound together, thus it is less affected by the skin effect and proximity effect.

[0038]

[0039] In the formula, k is the number of Litz strands, and d str For single strand diameter, r avg Let δ be the average line diameter and δ be the skin depth. R is the conductor spacing. ac ρ is the AC resistance, ρ is the resistivity, and N is the number of turns.

[0040] Step S6: Calculate the coupling coefficient between the coupled coils and analyze the frequency splitting to establish constraints. The coupling coefficient is calculated using the relationship between mutual inductance and the self-inductance of the two coils.

[0041]

[0042] In the formula, M is the mutual inductance of the coils, and L1 and L2 represent the self-inductance of coil one and coil two, respectively.

[0043] The coupling strength reflects, to some extent, how much of a changing magnetic field is transmitted from the transmitter to the receiver. The coupling coefficient indicates the tightness of the coupling between the primary and secondary coils. When k = 1, the components are tightly coupled, and the coupling coefficient of the power transformer is close to 1. When k = 0, it means that there is no coupling between the coils, and they are independent of each other.

[0044] Frequency splitting is a relatively common problem in MCR-WPT systems. Frequency splitting refers to the phenomenon where the resonant point splits from a single extreme point into two extreme points at the original resonant frequency, leading to a decrease in transmission efficiency at the original resonant point. In the design and practical application of MCR-WPT systems, to achieve effective coupling between the two circuits and good loop matching, the coils at the transmitting and receiving ends should have the same specifications and parameters, ensuring the consistency of the resonant capacitance value. The critical coupling coefficient for SS is:

[0045]

[0046] The formula for calculating the quality factor Q is:

[0047] In the MCR-WPT system, when k > k, the system is overcoupled; when k = k, the system is critical.

[0048] Coupling occurs when k < k, indicating undercoupling of the system. Coupling occurs when the degree of coupling between the coupled coils exceeds the system's critical coupling point.

[0049] The system's resonant frequency will split from its original single maximum point into two maximum points, resulting in a double-peak characteristic in the output coil. When the system's operating frequency is at one of the two maximum points after the split, the system's efficiency will increase; conversely, when the system's operating frequency is at the original resonant point, the system's efficiency will decrease.

[0050] Step S7: Calculate the self-inductance, mutual inductance, resistance, coupling coefficient, and transmission efficiency of the coil according to the set range of coupling coil parameters.

[0051] The specific wire diameter, screw diameter, spacing, and power frequency of the corresponding coil can be deduced from the maximum transmission efficiency.

[0052] The power supply frequency, wire diameter of the micro-planar coil, pitch, and spacing between the two coils are used as optimization variables; the energy transfer efficiency is used as the objective function value and optimization objective.

[0053] Step S8: Set constraint conditions based on the critical coupling coefficient: k≤k s And adjust the parameter range according to the constraints.

[0054] Step S9: Based on the coil setting parameters, the improved four-vector optimization algorithm is used to optimize the energy transfer efficiency, i.e., the objective function.

[0055] Using the maximum transmission efficiency formula as the objective function, and the resonant frequency, coil outer diameter, inner diameter, single-strand wire diameter, coil spacing, and number of coil turns as known parameters, an improved four-vector optimization algorithm is used to optimize the objective function, calculating the coil's self-inductance, mutual inductance, resistance, and coupling coefficient. The specific values ​​for the resonant frequency, coil outer diameter, inner diameter, single-strand wire diameter, coil spacing, and number of coil turns are then determined for the objective function at maximum efficiency.

[0056] Step S91: Initialize the population data using SPM chaotic mapping according to the set parameters, generate the initial population positions as evenly as possible within the constraints, and calculate the fitness of each individual in the population.

[0057] Step S92: Determine the four vectors that will serve as the initial leaders, and select the four individuals with the smallest fitness values ​​after initialization as the initial leaders;

[0058] Step S93: Randomly match each individual in the population as a parent using a cross-hatching strategy to generate new offspring and retain individuals with lower fitness values, and update the population position for the first time.

[0059] Step S94: Select the four individuals with the smallest fitness values ​​as the four-vector positions of the leader. Update the position of the best agent according to the motion equation of the four vectors after Gaussian perturbation. Finally, select the average position of the four best agents to update the population position for the second time.

[0060] Step S95: Determine whether the population iteration count has reached the maximum iteration count; if yes, output the result and end the iteration; if no, continue to repeat steps S94 to S95.

[0061] In the improved four-vector optimization algorithm, the principle is to guide the search strategy by using four best-performing leaders in the population, ensuring a balance between exploration and utilization in the search space, avoiding local minima, and mitigating the problem of slow convergence. During the optimization process, each leader is a potential solution, and new leaders are gradually replaced as fitness changes during iteration. The problem is optimized by numerically simulating the four vectors continuously leading the population through updates: In the population initialization phase, SPM chaotic mapping is introduced to reduce the randomness of generating the initial population, increase population diversity, and enable rapid convergence to obtain the global optimum; in the position update phase, a cross-linking strategy based on a genetic algorithm is introduced to achieve global search and prevent premature convergence; dynamic adaptive coefficients allow for greater exploration in the early stages and gradual refinement in later stages; a slight Gaussian perturbation is added to increase randomness and increase the probability of finding the global optimum; including:

[0062] SPM chaotic mapping:

[0063] Population initialization is typically done randomly, but chaotic mapping is a common and better initialization method. The chaotic sequence generated by SPM chaotic mapping is relatively uniform, possesses ergodicity and randomness, which helps the algorithm explore the search space more extensively. The expression is:

[0064]

[0065] In the formula, mod is the modulus of the mapping function, x(i) is the individual position, x(i+1) is the new individual position, and r is a random number between 0 and 1, used to introduce randomness into the mapping function and increase the unpredictability of the sequence; η and μ are control parameters, both with values ​​between 0 and 1; used to determine the segmentation of the mapping function, affecting the distribution and randomness of the chaotic sequence;

[0066] Cross-sectional strategy:

[0067] The cross-sectional strategy includes horizontal and vertical cross-sectional ...

[0068]

[0069] In the formula SM i1 and SM i2 It is the parent individual after pairing, and its offspring are and SM i1j and SM i2j They represent SM respectively i1 and SM i2 The j-th dimension, j = 1, 2, ..., dim, dim is the dimension, r1 and r2 are random numbers between (0, 1), and c1 and c2 are random numbers between (-1, 1);

[0070] Vertical crossover helps certain stagnant dimensions of the population escape premature convergence, thus allowing the algorithm to escape local optima. The expression is:

[0071]

[0072] In the formula SM ij1 and SM ij2 It is the parent individual after pairing, and its offspring are r is a random number between (0, 1).

[0073] Dynamic adaptive coefficients and slight Gaussian perturbations:

[0074] The adaptive coefficient α is one of the core mechanisms of the algorithm. It is responsible for adjusting the step size during the search process, thereby balancing exploration and utilization, and directly affecting whether the algorithm can effectively find the global optimum. The non-linear, dynamically updated adaptive coefficient allows the algorithm to be more exploratory in the early stages and gradually refines its approach in later stages. The expression is:

[0075] α(t)=α0×exp(-β×t)

[0076] In the formula, β is the decay rate and t is the current iteration number;

[0077] Since the four leader vectors guide the update of the entire population and select the top four optimal solutions during the algorithm's convergence phase, the four-vector update mechanism is one of the keys to avoiding getting trapped in local optima. Therefore, a Gaussian perturbation is introduced during position updates to increase randomness and the probability of finding the global optimum; the expression is:

[0078]

[0079] In the formula X n,iP represents the update position of the nth optimal agent in dimension i, where n ranges from 1 to 4; n,i It is the current position of the nth best agent in dimension i; This represents the average position of all agents in the i-th dimension. This represents the center position of the nth optimal agent and all agents in the i-th dimension. The absolute distance between them; α(t) is the adaptive coefficient. ξ1, ξ2, ξ3 represent random numbers uniformly distributed in [0,1]; η is the Gaussian perturbation, expressed as:

[0080] η = σ × N(0, 1)

[0081] In the formula, σ is the intensity of the disturbance, and N(0,1) represents a normal distribution with a mean of 0 and a variance of 1.

[0082] Based on the optimization results, a detailed simulation analysis of the MCR-WPT system was conducted using MAXWELL electromagnetic simulation software to verify the effectiveness of the optimized parameters. Finite element analysis can largely simulate actual conditions, reducing costs and allowing for early optimization of the design prototype. Specifically, the optimized coupling coil structure parameters ranged from a power frequency of 50kHz to 150kHz, a coil wire diameter of 0.1mm to 1mm, a pitch of 0.01mm to 1mm, a spacing of 3mm to 5mm, an outer diameter of 30mm, and an inner diameter of 6mm.

[0083] The embodiments described above do not constitute a limitation on the scope of protection of this application.

Claims

1. A method for optimizing the structure parameters of a planar coil in a MCR-WPT system based on an improved four-vector optimization algorithm, characterized in that, The method comprises: Step S1, analyzing the S-S topology compensation structure network, and deducing the energy transmission efficiency of the MCR-WPT system; Step S2: analyzing the influence of the coil physical structure on the coil characteristic parameters, including: self-inductance, mutual inductance, resistance, coupling coefficient; Step S3: calculating the self-inductance value of the coil; Step S4: calculating the mutual inductance coefficient value between the coupled coils; Step S5: calculating the alternating current resistance of the Litz wire under high-frequency alternating current; Step S6: calculating the coupling coefficient between the coupled coils, and analyzing the frequency splitting to establish a constraint condition; Step S6: determining the optimization variable, taking the energy transmission efficiency as the objective function value and the optimization target; Step S8: Set a constraint condition according to the critical coupling coefficient: k≤k s and adjust the parameter range according to the constraint condition; Step S9: according to the coil setting parameters, using the improved four-vector optimization algorithm to optimize the energy transmission efficiency, that is, the objective function; Step S9: according to the coil setting parameters, using the improved four-vector optimization algorithm to optimize the energy transmission efficiency, that is, the objective function, including: Taking the maximum transmission efficiency formula as the objective function, taking the resonant frequency, the coil outer diameter, the coil inner diameter, the single wire diameter, the coil spacing and the coil turns as the known parameter range, using the improved four-vector optimization algorithm to optimize the objective function, calculating the self-inductance, mutual inductance, resistance and coupling coefficient of the coil; the specific values of the resonant frequency, the coil outer diameter, the coil inner diameter, the single wire diameter, the coil spacing and the coil turns under the maximum efficiency are calculated; The optimization method comprises: Step S91: according to the set parameters, using SPM chaotic mapping to initialize the population data, generating initial population positions as evenly as possible within the constraint range, and calculating the fitness of each individual in the population; Step S92: determine the four vectors as the initial leaders, and select the positions of the four individuals with the smallest fitness values in the initialized population as the initial leaders; Step S93: through the vertical and horizontal cross strategy, randomly match each individual in the population as the parent to generate new offspring and retain the individuals with smaller fitness values, and update the population position for the first time; Step S94: select the positions of the four individuals with the smallest fitness values as the four vectors of the leaders, update the positions of the best agents according to the motion equation after the Gaussian disturbance of the four vectors, and finally select the average position of the positions of the four best agents to update the population position for the second time; Step S95: determine whether the iteration number of the population reaches the maximum iteration number; if yes, output the result and end the iteration; if not, continue to repeat steps S94 to S95; In the population initialization stage of the four-vector optimization algorithm, SPM chaotic mapping is introduced to reduce the randomness of generating the initial population, in the position updating stage of the algorithm, the vertical and horizontal cross strategy based on the genetic algorithm is introduced to realize the global search of the algorithm and avoid the premature convergence of the algorithm; through the dynamic adaptive coefficient, the algorithm has greater exploratory ability in the early stage and gradually becomes more refined in the later stage; adding slight Gaussian disturbance increases randomness and increases the probability of finding the global optimal solution.

2. The method of claim 1, wherein, Step S1, analyzing the S-S topology compensation structure network, and deducing the energy transmission efficiency of the MCR-WPT system; including The optimal parameters of the coil structure are obtained by using the improved four-vector optimization algorithm according to the parameters of the coupling coil, and the energy transmission efficiency formula of the MCR-WPT system, i.e., the objective function, is: where η represents the energy transmission efficiency of the system; ω is the resonance angular frequency of the system; M is the mutual inductance value of the coupling coils; R1, R2 represent the internal resistance of the primary and secondary coils, respectively; R L represents the load size of the system.

3. The method of claim 1, wherein, In step S3, the self-inductance of the coil is determined by the following method: where L is the self-inductance, N is the number of turns, μ0is the vacuum permeability, r avg is the average wire diameter r max is the outer radius of the coil, r min is the inner radius of the coil, C1= 2.46, C2= 0.

2.

4. The method of claim 1, wherein, In step S4, the mutual inductance coefficient between the coupling coils is determined by the following method: where M is mutual inductance, μ0 is vacuum permeability, N r is the number of turns of the primary coil, N t is the number of turns of the secondary coil, r r is the average radius of the primary coil, r t is the average radius of the secondary coil, and h is the distance between the coils.

5. The method of claim 1, wherein, In step S5, the AC resistance of the Litz wire under high-frequency AC is determined by the following method: where L K is the number of Litz strands, d str is the diameter of a single strand, r avg is the average wire diameter δ is the skin depth, is the wire spacing, R ac is the AC resistance, p is the resistivity, and N is the number of turns.

6. The method of claim 3, wherein, Step S6: Calculate the coupling coefficient between the coupling coils, analyze the frequency splitting to establish the constraint conditions, including: The coupling coefficient is obtained by the relationship between the mutual inductance and the self-inductance of the two coils: In the formula, M is the mutual inductance of the coil, L1 and L2 represent the self-inductance of coil one and coil two, respectively; The coupling coefficient represents the coupling tightness between the primary coil and the secondary coil; when k=1, the elements are tightly coupled, and the coupling coefficient of the power transformer is close to 1; when k=0, it means that there is no coupling between the coils, and they are independent of each other; The coils of the transmitting end and the receiving end have the same specifications and parameters, ensuring the consistency of the values of the resonance capacitors; the critical coupling coefficient of S-S is: where the quality factor Q is calculated by the formula: In the MCR-WPT system, when k>k s , the system is in over-coupling, when k=k s , the system is in critical coupling, and when k<k s , the system is in under-coupling.

7. The method of claim 1, wherein, Step S7, including: According to the set range of the coupling coil parameters, the self-inductance, mutual inductance, resistance, coupling coefficient and transmission efficiency of the coil are calculated; According to the maximum transmission efficiency, the specific wire diameter, pitch diameter, spacing and power frequency of the corresponding coil are deduced; The power frequency, wire diameter and pitch of the micro-plane coil, and the spacing between the two coils are used as optimization variables; the energy transmission efficiency is used as the objective function value and optimization target.

8. The method of claim 1, wherein, The SPM chaotic mapping expression is: In the formula, mod is the function module, x(i) is the individual position, x(i+1) is the new individual position, r is a random number between 0 and 1, which is used to introduce randomness in the mapping function and increase the unpredictability of the sequence; η and μ are control parameters, both of which are between 0 and 1.

9. The method of claim 1, wherein, The cross strategy includes horizontal and vertical cross, and the expression is: where SM i1 and SM i2 are the paired parent individuals, whose offspring is and SM i1j and SM i2j denote the j-th dimension of SM i1 and SM i2 , respectively, j = 1, 2, …, dim, dim is the dimension, r1 and r2 are random numbers between (0, 1), and c1 and c2 are random numbers between (-1, 1). The vertical cross promotes some stagnation dimensions of the population to escape from dimension premature convergence, so that the algorithm jumps out of the local optimum, and the expression is: where SM ij1 and SM ij2 are the paired parent individuals whose offspring is r is a random number between (0, 1).

Images