A method for modeling and optimizing a multi-coil wireless energy transfer system

Abstract

The application discloses a modeling and optimization method of a multi-coil wireless energy transmission system, and establishes a model of self-inductance, high-frequency alternating current resistance, mutual inductance and the whole transmission system of the wireless energy transmission system, iterates system parameters by using a genetic algorithm under a set constraint condition, obtains optimal system parameters of the multi-coil wireless energy transmission system under maximum efficiency, and thus the modeling of the multi-coil wireless energy transmission system is established.

Description

Technical Field

[0001] This invention belongs to the field of wireless power transfer technology, and more specifically, relates to a modeling and optimization method for a multi-coil wireless power transfer system. Background Technology

[0002] Wireless Power Transfer (WPT) technology is a flexible, convenient, safe, and potentially automated technology. Compared to wired transmission systems, WPT eliminates the need for power plugs, sockets, wires, and other direct wired connections. It also offers superior flexibility, safety, and lifespan in harsh environments. WPT effectively solves the problems of frequent plugging and unplugging in wired systems and the danger of electric shock from bare wires, while reducing the weight and size of wired systems, thus saving space and cost.

[0003] Based on the aforementioned advantages of the WPT system, various fields have conducted research and exploration into it. Future research on WPT systems will primarily focus on improving the overall system transmission efficiency. However, in WPT systems, the coupling between various electrical parameters is relatively strong; a change in one physical parameter can affect the parameters of the entire system. Therefore, optimal system design is urgently needed. The design of WPT systems focuses on three main aspects: coil modeling and selection, system modeling and electrical characteristic analysis, and system optimization for maximum power or optimal efficiency.

[0004] Regarding the modeling and design of high-frequency coils, the literature "Kim JJ, Kim J. Modeling method of coil module for wireless power transfer system by two-port S-parameter measurement in frequency domain[C]. 2014 IEEE Wireless Power Transfer Conference, Jeju, Korea (South), 2014: 251-254." uses two-port S-parameter theory to model the coil self-inductance, coil internal resistance, and magnetic coupling coefficient for PCB coils, with an error within 2%. In the literature “Cho J, Sun J, Kim H, et al. Coil design for 100kHz and 6.78MHz wpt system: Litz and solid wires and winding methods[C]. 2017 IEEE International Symposium on Electromagnetic Compatibility Signal / Power Integrity (EMCSI), Washington, DC, USA, 2017: 803-806,” an optimal winding method for coils from 100kHz to 6.78MHz was studied using Litz wire and electromagnetic simulation to obtain a high coil quality factor. The literature “Qian L, Chen M, Cui K, et al. Modeling of mutual inductance between two misalignment planar coils in wireless power transfer[J]. IEEE Microwave and Wireless Components Letters, 2020, 30(8): 814-817,” proposed a modeling method for mutual inductance between a pair of planar helical coils with lateral and angular misalignment. The result showed an error of less than 15.1% compared to the 3D electromagnetic simulation. The literature “Fan Xingming, Gao Linlin, Su Binhua, Tang Fuhong, Zhang Xin. Simulation Modeling Analysis of MCR-WPT Transmitter / Receiver Coil Performance [J]. Control Engineering, 2020, 27(12):2151-2157” takes the equivalent circuit of two coils as the research object and proposes to replace solid wires with the same outer diameter with copper tubes.

[0005] Current optimization methods for WPT systems include coil modeling optimization, direct coil optimization, and system efficiency or power optimization. The paper "Yadav P, Veerachary M. Auxiliary coils assisted inductance enhancement in the wireless power transfer schemes[C]. 2020 IEEE International Conference on Computing, Power and Communication Technologies (GUCON), Greater Noida, India, 2020:245-249." proposes a new WPT coil structure that utilizes Ansys Maxwell and PSIM to improve the coupling coefficient of circular and rectangular coils. The paper "Hariri A, Elsayed A, Mohammed O A. An integrated characterization model and multi-objective optimization for the design of an ev charger's circular wireless powertransfer pads[J]. IEEE Transactions on Magnetics, 2017, 53(6):1-4." optimizes system efficiency based on an optimization method with three variables and four constraints. The literature “Chen Y, Zhang H, Shin CS, et al. An efficiency optimization-based asymmetric tuning method of double-sided LCC compensated wpt system for electric vehicles[J].IEEE Transactions on Power Electronics,2020,35(11):11475-11487” applies LLC compensation to optimize the efficiency of the WPT system.The literature “Abatti PJ, Miranda C, Silva M, et al. Analysis and optimization of three-coil wireless power transfer systems[J].IET Power Electronics,2018,11(1):68-72” analyzes three-coil WPT systems from the perspectives of power supply, transmission, and load circuits, and proposes methods for optimizing efficiency and power.

[0006] The coil modeling methods described in the above literature all require complex electromagnetic simulation software. Changing a certain parameter requires re-simulating, which leads to time-consuming and labor-intensive simulations or insufficient accuracy. However, if the error is too large, it does not help the modeling enough, resulting in an incomplete model. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art and provide a modeling and optimization method for a multi-coil wireless power transmission system. The method mainly uses the modeling of the high-frequency AC resistance, inductance, and mutual inductance of the coils to form a model from the most basic physical material geometric parameters to the final wireless power transmission system model, thereby simplifying the design of the wireless power transmission system and achieving the optimization of the geometric parameters in the wireless power transmission system.

[0008] To achieve the above-mentioned objectives, the present invention provides a modeling and optimization method for a multi-coil wireless power transfer system, characterized by comprising the following steps:

[0009] (1) Construct a self-inductance model of the coil;

[0010] (2) Construct an AC resistance model for the coil, taking into account the skin effect and proximity effect;

[0011] (3) Construct a mutual inductance model of the coils;

[0012] (4) Construct a multi-coil wireless power transmission system model;

[0013] (5) Construct the objective function and constraints of the multi-coil wireless power transfer system;

[0014] (6) Write the model, objective function and constraints established in steps (1)-(5) into the simulation tool MATLAB. Then, with the objective function as the objective and under the constraints, iterate the parameters of the multi-coil wireless power transmission system by calling the genetic algorithm in MATLAB, thereby outputting the optimized multi-coil wireless power transmission system.

[0015] The objective of this invention is achieved as follows:

[0016] This invention provides a modeling and optimization method for a multi-coil wireless power transmission system. The method establishes models of the coil self-inductance, high-frequency AC resistance, mutual inductance, and the entire transmission system. Under set constraints, with the efficiency of the multi-coil wireless power transmission system as the objective, a genetic algorithm is used to iterate the system parameters to obtain the optimal system parameters for the multi-coil wireless power transmission system at maximum efficiency, thereby establishing the model of the multi-coil wireless power transmission system.

[0017] Meanwhile, the modeling and optimization method for a multi-coil wireless power transfer system of the present invention also has the following beneficial effects:

[0018] (1) This invention realizes the mathematical modeling of high-frequency resistance, self-inductance and mutual inductance of high-precision cylindrical spiral coils and planar spiral coils.

[0019] (2) This invention uses MATLAB to perform step-by-step modeling design of the wireless power transmission system, from coil modeling to system analysis and then to system optimization, realizing the integration of modeling, design and optimization. Compared with the modeling method using electromagnetic simulation software, it is more convenient and mature. Attached Figure Description

[0020] Figure 1 This is a flowchart of a modeling and optimization method for a multi-coil wireless power transmission system according to the present invention;

[0021] Figure 2 This is a schematic diagram of the coil structure;

[0022] Figure 3 This is a schematic diagram of the structure for calculating the mutual inductance of cylindrical coils;

[0023] Figure 4 It is the equivalent circuit of a cylindrical four-coil WPT system;

[0024] Figure 5 This is the result of efficiency optimization for a cylindrical four-coil WPT system with an output power of 100W; Detailed Implementation

[0025] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be particularly noted that in the following description, detailed descriptions of known functions and designs that might obscure the main content of the invention will be omitted here.

[0026] Example

[0027] Figure 1 This is a flowchart of a modeling and optimization method for a multi-coil wireless power transmission system according to the present invention.

[0028] In this embodiment, as Figure 1 As shown, the present invention provides a modeling and optimization method for a multi-coil wireless power transfer system, comprising the following steps:

[0029] S1. Construct a self-inductance model of the coil;

[0030] In this embodiment, the coils selected for the multi-coil wireless power transfer system are typically cylindrical helical coils or planar helical coils, such as... Figure 2 As shown, where, Figure 2 (a) is a schematic diagram of a cylindrical helical coil. Figure 2 (b) is a schematic diagram of a planar helical coil;

[0031] Independent self-inductance models need to be established for the two types of coils mentioned above. When a cylindrical helical coil is used, the corresponding self-inductance model is as follows:

[0032]

[0033] Where i represents the coil number, L i Let r be the self-inductance of the i-th coil. i Let N be the radius of the i-th coil. i Let l be the number of turns of the i-th coil. i Let K be the length of the i-th coil. ni Let k be the Nagaoka coefficient of the i-th coil. i and To calculate the required intermediate variables, K(k) i ) is k i The first complete integral of the elliptic, E(k) i ) is k i The second complete integral of the elliptic;

[0034] When a planar helical coil is selected, the corresponding self-inductance model is:

[0035]

[0036] Among them, L i Let a be the self-inductance of the i-th coil. i Let ca represent the geometric radius of the i-th coil. i P is the pitch of the i-th coil. i The diameter of the wires that make up the coil The ratio of N i Let r be the number of turns of the i-th coil. oi D is the distance from the center reference point of the i-th coil to the center of the wire in the last loop. oi D Ii It is an intermediate variable.

[0037] S2. Construct a resistance model for the coil, taking into account the skin effect and proximity effect.

[0038] In this embodiment, the resistance models for both planar helical coils and cylindrical helical coils are consistent; specifically, the model used is as follows:

[0039]

[0040] Among them, R i To account for the resistance of the i-th coil under the skin effect and proximity effect, let σ be the conductivity of the wires constituting the coil, μ be the permeability of free space, and d be the resistance of the ith coil. i Let be the diameter of the i-th coil. R is the diameter of the wires forming the coil, ω is the angular frequency of the multi-coil wireless power transfer system, and R is the diameter of the wires forming the coil. Ti R Pi R Oi R Ki As an intermediate variable;

[0041] S3. Construct a mutual inductance model of the coils;

[0042] In this embodiment, different mutual inductance models need to be established for different types of coils, such as... Figure 3 As shown, when selected Figure 3 When the cylindrical helical coils shown in the diagram exhibit mutual inductance, their mutual inductance model is as follows:

[0043]

[0044] Among them, M ij The number of turns of the coil is N i The i-th coil and the number of coil turns are N j The mutual inductance between the j-th coils, in this invention, M ij With M ji Equal, with the same numerical value. T ij The mutual inductance between a single turn of the i-th coil and the j-th coil is obtained by summing these values ​​to get M. ij r i Let r be the radius of the i-th coil. j Let m be the radius of the j-th coil. ij To calculate the required intermediate variables, K(m) ij ) and E(m ij ) are about m ij The first and second elliptic integrals, For the i-th coil The center of the conductor of the j-th coil and the first coil in the j-th coil The distance between the centers of the coiled conductors The value range is 1-N i , The value range is 1-N j offset ij P is the offset between the i-th coil and the j-th coil. i ,P j These are the pitches of the i-th and j-th coils, respectively;

[0045] When a planar helical coil is selected, its mutual inductance model is as follows:

[0046]

[0047] Among them, M ij The number of turns of the coil is N i The i-th coil and the number of coil turns are N j The mutual inductance between the j-th coils, in this invention, M ij With M ji Equal, numerically equal; T ij The mutual inductance between a single turn of the i-th coil and the j-th coil is obtained by summing these values ​​to get M. ij m ij To calculate the required intermediate variables, K(m) ij ) and E(m ij ) are about m ij The first and second elliptic integrals, Let e1 be the distance between the i-th coil and the j-th coil, and let e1 represent the distance between the i-th coil and the j-th coil. The distance between the center of the conductor of the i-th coil and the central axis of the i-th planar helical coil, e2 represents the distance between the center of the j-th coil and the central axis of the i-th coil. The distance P between the center of the conductor of the j-th coil and the central axis of the j-th coil. i ,P j Let r be the pitch of the i-th coil and the j-th coil, respectively. i Let r be the radius of the i-th coil. j Let be the radius of the j-th coil. The value range is 1-N i , The value range is 1-N j ;

[0048] S4. Construct a model of a multi-coil wireless power transfer system;

[0049]

[0050] Where n is the number of coils, and the value of n ranges from 2 to 4, meaning this model is applicable to two-coil, three-coil, and four-coil systems. Z i R represents the impedance of the i-th loop in a multi-coil wireless power transfer system. SR is the internal resistance of the power supply. L R is the load resistance. i Let L be the equivalent impedance of the i-th coil. i Let C be the inductance of the i-th coil. i Let I be the resonant capacitance of the i-th coil. i Let M be the current in the i-th loop containing the i-th coil, i = 1, 2, ..., n. ij V represents the mutual inductance between the i-th coil and the j-th coil. S This is the power supply voltage.

[0051] In this embodiment, taking a cylindrical four-coil wireless power transmission system as an example, when n=4, the following model is obtained:

[0052]

[0053] Figure 4 The diagram shows the equivalent circuit of a cylindrical four-coil wireless power transfer system. Figure 4 As shown, resonant capacitors C1 and C4 are taken to be infinite, that is... and Two items do not exist. Z1-Z4 represent the impedances of loops 1-4 respectively, I1-I4 represent the currents of loops 1-4 respectively, L1-L4 represent the inductances of coils 1-4 respectively, R1-R4 represent the resistances of coils 1-4 respectively, C2 is the resonant capacitance of coil 2, C3 is the resonant capacitance of coil 3, M 12 M represents the mutual inductance between the first and second coils. 21 and M 12 Same, M 13 M 31 M 14 M 41 M 23 M 32 M 24 M 42 M 34 M 43 Both represent the mutual inductance between the coils corresponding to their numerical subscripts, V S R is the power supply voltage. S This is the internal resistance of the power supply.

[0054] S5. Construct the objective function and constraints for a cylindrical four-coil wireless power transmission system;

[0055] S5.1 Construct the objective function of a cylindrical four-coil wireless power transmission system;

[0056]

[0057]

[0058]

[0059]

[0060] Where η is the output efficiency of the cylindrical four-coil wireless power transfer system, and P IN P is the input power of the cylindrical four-coil wireless power transfer system. OUT V represents the output power of the cylindrical four-coil wireless power transfer system. OUT Let I be the output voltage of the cylindrical four-coil wireless power transmission system, abs(·) represents the absolute value, Re(·) represents the real part, I1 is the current in the first loop, and I4 is the current in the fourth loop.

[0061] S5.2 Establish the constraints for the cylindrical four-coil wireless power transmission system;

[0062] Constraints include linear constraints and nonlinear constraints;

[0063] The linear constraint condition is as follows:

[0064] X(x 1LOW ,x 2LOW ,...,x 21LOW )≤X(x1,x2,...,x 21 )≤X(x 1HIGH ,x 2HIGH ,...,x 21HIGH )

[0065] Where x1,x2,...,x 21 This represents the parameters to be optimized in the cylindrical four-coil wireless power transfer system, x. 1LOW ,x 2LOW ,...,x 21LOW Representing x1, x2, ..., x 21 The lower limit values ​​corresponding to each parameter, x 1HIGH ,x 2HIGH ,...,x 21HIGH Representing x1, x2, ..., x 21 The upper limit values ​​corresponding to each parameter in the table, where X(·) represents the parameter set;

[0066] In this embodiment, for a specific cylindrical four-coil wireless power transmission system, the 23 parameters that need to be optimized are as follows: x1 is the system frequency, x2-x5 are the diameters of the conductors constituting the first to fourth coils, x6-x9 are the ca values ​​of the first to fourth coils, and x... 10 -x 13 The diameters of the first through fourth coils are respectively, x14 -x 17 These represent the number of turns for the 1st to 4th coils, respectively, x 18 x is the distance between the first and second coils. 19 x is the distance between the second and third coils. 20 x is the distance between the 3rd and 4th coils. 21 For load.

[0067] The nonlinear constraint conditions are:

[0068]

[0069] Among them, P LOW and P HIGH The output power P is respectively OUT The lower and upper limits of V LOW and V HIGH The output voltage V is respectively OUT The lower and upper limits.

[0070] S6. Write the model, objective function and constraints established in steps S1-S5 into the simulation tool MATLAB. Then, with the objective function as the objective and under the constraints, iterate the parameters of the multi-coil wireless power transmission system by calling the genetic algorithm in MATLAB, thereby outputting the optimized multi-coil wireless power transmission system.

[0071] In this embodiment, the DC power supply voltage is set to 48V, the internal resistance of the power supply is 0Ω, the output voltage range is set to 39V-40V, and the output power range is set to 99W-101W. Simulation shows that after optimization by the genetic algorithm, the system has a maximum efficiency of 87.85%, an output power of 100W, an output voltage of 40.08V, and an optimal operating frequency of 440kHz. Figure 5 (a) Curves of system efficiency versus frequency and output power versus frequency, plotted under the optimal system parameters obtained after optimization, with only the frequency changed. Figure 5 (b) shows the curves of system efficiency versus frequency and output voltage versus frequency when only the frequency is changed under the optimal system parameters obtained after optimization.

[0072] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A modeling and optimization method for a multi-coil wireless power transfer system, characterized in that, Includes the following steps: (1) Construct a self-inductance model of the coil; The coil can be a cylindrical spiral coil or a planar spiral coil; When a cylindrical spiral coil is selected, the corresponding self-inductance model is: ； in, Represents the coil number. For the first The self-inductance of the coil, For the first The radius of each coil, For the first The number of turns of each coil, For the first The length of each coil, For the first The Nagaoka coefficient of each coil, and To calculate the necessary intermediate variables, for The first complete integral of the elliptic, for The second complete integral of the elliptic; When a planar helical coil is selected, the corresponding self-inductance model is: ； in, For the first The self-inductance of the coil, Indicates the first The geometric radius of each coil, For the first The pitch of each coil The diameter of the wires that make up the coil The ratio, For the first The number of turns of each coil, For the first The distance from the center reference point of each coil to the center of the last coil of wire. As an intermediate variable; (2) Construct a resistance model for the coil, taking into account the skin effect and proximity effect; (3) Construct a mutual inductance model of the coils; (4) Construct a model of a multi-coil wireless power transfer system; ； in, The number of coils In a multi-coil wireless power transfer system, the first... The impedance of each circuit, The internal resistance of the power supply For load resistance, For the first The equivalent impedance of each coil, For the first The inductance of the coil, For the first The resonant capacitance of each coil, For the first The coil is located in the first Current in each loop , For the first The coil and the first Mutual inductance between coils This is the power supply voltage. The angular frequency of a multi-coil wireless power transfer system; (5) Construct the objective function and constraints of the multi-coil wireless power transfer system; (6) Write the model, objective function and constraints established in steps (1)-(5) into the simulation tool MATLAB. Then, with the objective function as the objective and under the constraints, iterate the parameters of the multi-coil wireless power transmission system by calling the genetic algorithm in MATLAB, thereby outputting the optimized multi-coil wireless power transmission system.

2. The modeling and optimization method for a multi-coil wireless power transfer system according to claim 1, characterized in that, The resistance model of the coil is: ； in, To consider the skin effect and proximity effect, the first The resistance of each coil, The conductivity of the wires that make up the coil, The permeability of free space, For the first The diameter of each coil, The diameter of the wire that makes up the coil, For multi-coil wireless power transfer systems, the angular frequency is... , , , It is an intermediate variable.

3. The modeling and optimization method for a multi-coil wireless power transfer system according to claim 1, characterized in that, The mutual inductance model of the coils is selected from either the mutual inductance model of a cylindrical spiral coil or the mutual inductance model of a planar spiral coil. The mutual inductance model of the cylindrical helical coil is as follows: ； in, The number of turns of the coil is The The number of coils and the number of coil turns are: The Mutual inductance between coils For the first The coil and the first The mutual inductance between single-turn coils of each coil For the first The radius of each coil, For the first The radius of each coil, As an intermediate variable, and They are about The first and second elliptic integrals, For the first The first coil The center of the loop and the first The first coil The distance between the centers of the coiled conductors The range of values ​​is , The range of values ​​is , For the first The coil and the first The offset between the coils The first The coil and the first The pitch of each coil; The mutual inductance model of a planar helical coil is as follows: ； in, The number of turns of the coil is The The number of coils and the number of coil turns are: The Mutual inductance between coils For the first The coil and the first The mutual inductance between single-turn coils of each coil As an intermediate variable, and They are about The first and second elliptic integrals, For the first The coil and the first The distance between the coils Indicates the first The first coil The center of the conductor of the loop and the first The distance between the central axes of the coils Indicates the first The first coil The center of the conductor of the loop and the first The distance between the central axes of the coils The first The coil and the first The pitch of each coil, For the first The radius of each coil, For the first The radius of each coil, The range of values ​​is , The range of values ​​is .

4. The modeling and optimization method for a multi-coil wireless power transfer system according to claim 1, characterized in that, The objective function of the multi-coil wireless power transfer system is: ； in, For the output efficiency of multi-coil wireless power transfer systems, For the input power of a multi-coil wireless power transfer system, For the output power of a multi-coil wireless power transfer system, The output voltage of a multi-coil wireless power transfer system. This indicates taking the absolute value. Indicates taking the real part, This represents the current in the first loop. Indicates the first The current in each loop.

5. The modeling and optimization method for a multi-coil wireless power transfer system according to claim 1, characterized in that, The constraints of the multi-coil wireless power transfer system include linear constraints and nonlinear constraints. The linear constraint condition is as follows: ； in, This represents the parameters to be optimized for a multi-coil wireless power transfer system. express The lower limit values ​​corresponding to each parameter in the table. express The upper limit values ​​corresponding to each parameter in the table. Represents a set of parameters; The nonlinear constraint conditions are: ； in, and Output power The lower and upper limits, and Output voltage The lower and upper limits.

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