CN115577638A - Modeling and optimizing method of multi-coil wireless energy transmission system - Google Patents
Modeling and optimizing method of multi-coil wireless energy transmission system Download PDFInfo
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Abstract
The invention discloses a modeling and optimizing method of a multi-coil wireless energy transmission system, which comprises the steps of establishing a model of a wireless energy transmission system coil self-inductance, a high-frequency alternating current resistance, a mutual inductance and the whole transmission system, and utilizing a genetic algorithm to iterate system parameters by taking the efficiency of the multi-coil wireless energy transmission system as a target under a set constraint condition to obtain the optimal system parameters of the multi-coil wireless energy transmission system under the maximum efficiency, thereby establishing the modeling of the multi-coil wireless energy transmission system.
Description
Technical Field
The invention belongs to the technical field of wireless energy transmission, and particularly relates to a modeling and optimizing method of a multi-coil wireless energy transmission system.
Background
Wireless Power Transfer (WPT) technology is a flexible, convenient, safe, and potentially automated technology. Compared with a wired transmission system, the wireless energy transmission system does not need a power plug, a socket, a wire and other direct wired connection modes, and has better flexibility, safety and service life than the wired transmission system in severe environment. The WPT effectively solves the problem of frequent plugging of a wired system and the danger of electric shock of a bare wire, and reduces the quality and the volume of the wired system, thereby saving the space and the cost.
Based on the above advantages of the WPT system, research and exploration have been made on the WPT system in various fields. The main research direction for the WPT system in the future is to improve the transmission efficiency of the whole system. However, in the WPT system, the coupling of each electrical parameter is relatively strong, and the change of a certain physical parameter may affect the parameters of the whole system, so that the optimization design of the system needs to be solved urgently. In the design of WPT systems, the emphasis includes three aspects, respectively modeling and selection of coils, modeling and analysis of electrical characteristics of the system, and system optimization for maximum power or optimum efficiency.
In modeling and designing a high frequency coil, in the document "Kim J, kim J. Modeling method of coil module for Wireless Power Transfer system by two-port parameter measurement in frequency domain [ C ].2014IEEE Wireless Power Transfer conference, jeju, korea (South), 2014 251-254", the coil self-inductance, the coil internal resistance, and the magnetic coupling coefficient are modeled using the two-port S parameter theory for a PCB coil, and the error is within 2%. In the document "Cho J, sun J, kim H, et al. Coil design for 100khz and 6.78mhz wpt system. The document "Qian L, chen M, cui K, et al, modeling of a mutual inductance between planar coils in a Wireless power transfer [ J ]. IEEE Microwave and Wireless Components Letters,2020,30 (8): 814-817" proposes a mutual inductance modeling of a pair of planar spiral coils with lateral and angular offsets, the error with 3D electromagnetic simulation is more than 15.1%. The literature 'fanxing, gaolining, subin, tangfuhong, zhang Xin' MCR-WPT transmitting/receiving coil performance simulation modeling analysis [ J ] 'control engineering 2020,27 (12): 2151-2157' uses two-coil equivalent circuits as research objects and proposes that copper tubes replace solid wires with the same outer diameter.
The current optimization method for the WPT system comprises coil modeling optimization, direct coil optimization and system efficiency or power optimization. The document "Yadav P, vector M. Automatic coils assisted induced enhancement in the wireless power transfer schemes [ C ].2020IEEE International Conference on computing, power and Communication Technologies (GUCON), great Noida, india,2020 245-249" proposes a new WPT coil structure, which utilizes Ansys Maxwell and PSIM to improve the coupling coefficients of circular coils, rectangular coils, etc. The literature "Hariri A, elsayed A, mohammed O A. An integrated characterization model and multi-objective optimization for the design of an ev's circular with less power transfer pads [ J ]. IEEE Transactions on Magnetics,2017,53 (6): 1-4" four constraint optimization method based on three variables to optimize system efficiency. The document "Chen Y, zhang H, shin C S, et al, an effective-based estimation method of double-sized LCC compensated WPT systems for electronic devices [ J ]. IEEE Transactions on Power Electronics,2020,35 (11): 75-11487" optimization of WPT system efficiency using LLC compensation. The document "Absatti P J, miranda C, silva M, et al analysis and optimization of thread-less Power transfer systems [ J ]. IET Power Electronics,2018,11 (1): 68-72." for a three-coil WPT system, analysis is performed from three circuit loops of Power supply, transmission, and load, respectively, to propose an optimization method of efficiency and Power.
The coil modeling methods in the above documents all require complex electromagnetic simulation software, and simulation needs to be performed again when a certain parameter is changed, so that the simulation is time-consuming and labor-consuming or the accuracy is insufficient, but too large errors do not help the modeling sufficiently, so that the modeling is incomplete.
Disclosure of Invention
The modeling from the most basic physical material geometric parameters to the final modeling of the wireless energy transmission system is formed by taking the modeling of high-frequency alternating current resistance, inductance and mutual inductance of the coil as main means, so that the design of the wireless energy transmission system is simplified, and the optimization of the geometric parameters in the wireless energy transmission system is realized.
In order to achieve the above object, the present invention provides a modeling and optimizing method for a multi-coil wireless energy transmission system, comprising the steps of:
(1) Constructing a self-inductance model of the coil;
(2) Constructing an alternating current resistance model of the coil under the consideration of skin effect and proximity effect;
(3) Constructing a mutual inductance model of the coil;
(4) Constructing a multi-coil wireless energy transmission system model;
(5) Constructing an objective function and constraint conditions of the multi-coil wireless energy transmission system;
(6) Writing the model, the target function and the constraint condition established in the steps (1) - (5) into a simulation tool MATLAB, and then iterating the parameters of the multi-coil wireless energy transmission system by calling a genetic algorithm in the MATLAB under the constraint of the constraint condition by taking the target function as a target, thereby outputting the optimized multi-coil wireless energy transmission system.
The invention aims to realize the following steps:
the invention relates to a modeling and optimizing method of a multi-coil wireless energy transmission system, which comprises the steps of establishing a model of a wireless energy transmission system coil self-inductance, a high-frequency alternating current resistance, a mutual inductance and the whole transmission system, and iterating system parameters by using a genetic algorithm to obtain the optimal system parameters of the multi-coil wireless energy transmission system under the maximum efficiency under the set constraint condition by taking the efficiency of the multi-coil wireless energy transmission system as a target, so as to establish the modeling of the multi-coil wireless energy transmission system.
Meanwhile, the modeling and optimizing method of the multi-coil wireless energy transmission system further has the following beneficial effects:
(1) The invention realizes mathematical modeling of high-frequency resistance, self-inductance and mutual inductance of the high-precision cylindrical spiral coil and the planar spiral coil.
(2) The invention uses MATLAB to carry out step-by-step modeling design from coil modeling to system analysis and then to system optimization on the wireless energy transmission system, realizes integration of modeling, design and optimization, and is more convenient and mature compared with a modeling mode using electromagnetic simulation software.
Drawings
FIG. 1 is a flow chart of a method for modeling and optimizing a multi-coil wireless energy transfer system of the present invention;
FIG. 2 is a schematic diagram of a coil configuration;
FIG. 3 is a schematic diagram of a structure for calculating mutual inductance values of cylindrical coils;
figure 4 is an equivalent circuit of a cylindrical four coil WPT system;
figure 5 is the result of efficiency optimization for a cylindrical four coil WPT system with an output power of 100W;
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Examples
Fig. 1 is a flow chart of a modeling and optimizing method of a multi-coil wireless energy transmission system according to the present invention.
In this embodiment, as shown in fig. 1, the modeling and optimizing method of a multi-coil wireless energy transmission system of the present invention includes the following steps:
s1, constructing a self-inductance model of a coil;
in this embodiment, the coils selected for the multi-coil wireless energy transmission system are generally cylindrical spiral coils or planar spiral coils, as shown in fig. 2, wherein fig. 2 (a) is a schematic diagram of the cylindrical spiral coils, and fig. 2 (b) is a schematic diagram of the planar spiral coils;
for the two coils, independent self-inductance models need to be established, wherein when a cylindrical spiral coil is selected, the corresponding self-inductance models are as follows:
wherein i represents a coil number, L i Is the self-inductance of the ith coil, r i Radius of the i-th coil, N i Is the number of turns of the i-th coil, l i Is the length of the ith coil, K ni Is the Changan coefficient, k, of the ith coil i And
to calculate the required intermediate variables, K (K) i ) Is k i First complete integration of the ellipse of (c), E (k) i ) Is k is i Second full integration of the ellipse;
when the planar spiral coil is selected, the corresponding self-inductance model is as follows:
wherein L is i Is the self-inductance of the ith coil, a i Denotes the geometric radius, ca, of the ith coil i Is the pitch P of the ith coil i And the diameter of the wire constituting the coil
Ratio of (A) to (B), N i Number of turns of i-th coil, r oi Is the distance from the center reference point of the ith coil to the center of the last turn of the wire, D oi ,D Ii Is an intermediate variable.
S2, constructing a resistance model of the coil under the consideration of the skin effect and the proximity effect;
in this embodiment, the resistance models of the planar spiral coil and the cylindrical spiral coil are all consistent, and the specifically adopted models are as follows:
wherein R is i To consider the resistance of the ith coil under skin and proximity effects, σ is the electrical conductivity of the wire that makes up the coil, μ is the vacuum permeability, d i Is the diameter of the i-th coil,
omega is the angular frequency of the multi-coil wireless energy transfer system, R, for the diameter of the wire forming the coil Ti 、R Pi 、R Oi 、R Ki Is an intermediate variable;
s3, constructing a mutual inductance model of the coil;
in this embodiment, different mutual inductance models are established for different types of coils, as shown in fig. 3, when the structure of the cylindrical spiral coil shown in fig. 3 is selected for mutual inductance, the mutual inductance model of the cylindrical spiral coil is:
wherein, M ij The number of turns of the coil is N i The ith coil and the number of coil turns of N j In the present invention, M is the mutual inductance between the jth coils ij And M ji Equal, equal values. T is ij The mutual inductance between the single turn coils of the ith coil and the jth coil is obtained by adding up the mutual inductances ij ，r i Radius of the i-th coil, r j Radius of the jth coil, m ij To calculate the required intermediate variables, K (m) ij ) And E (m) ij ) Are respectively related to m ij The first and second elliptical integrals of (a),
is the ith coil
The center of the wire of the coil and the th coil of the jth coil
The distance between the centers of the coil conductors,
has a value in the range of 1-N i ，
Has a value range of 1-N j ，offset ij Is the offset between the ith and jth coils, P i ,P j The pitches of the ith coil and the jth coil respectively;
when the planar spiral coil is selected, the mutual inductance model is as follows:
wherein M is ij The number of turns of the coil is N i And the number of turns of the coil is N j In the present invention, M is the mutual inductance between the jth coils ij And M ji Equal, equal in value; t is a unit of ij The mutual inductance between the single turn coils of the ith coil and the jth coil is obtained by adding up the mutual inductances ij ，m ij To calculate the required intermediate variables, K (m) ij ) And E (m) ij ) Are respectively offAt m ij The first and second elliptical integrals of (a),
is the distance between the ith and jth coils, e 1 Indicating the ith in the ith coil
Distance between the center of the wire of the coil and the central axis of the ith planar helical coil, e 2 Denotes the th in the jth coil
Distance between center of coil wire and j central axis of coil, P i ,P j Pitch, r, of the ith and jth coils, respectively i Radius of the i-th coil, r j Is the radius of the jth coil,
has a value range of 1-N i ，
Has a value in the range of 1-N j ；
S4, constructing a multi-coil wireless energy transmission system model;
wherein n is the number of coils, the value range of n is 2-4, namely the model is suitable for two-coil, three-coil and four-coil systems, Z i Representing the impedance, R, of the ith loop in a multi-coil wireless energy transfer system S For internal resistance of power supply, R L Is a load resistance, R i Is the equivalent impedance of the ith coil, L i Inductance of the i-th coil, C i Is the resonant capacitance of the ith coil, I i I =1,2, \ 8230;, n, M, is the current in the ith loop in which the ith coil is located ij For the ith coil and the jth coilMutual inductance between coils, V S Is the supply voltage.
In this embodiment, taking a cylindrical four-coil wireless energy transmission system as an example, when n =4 is taken, the following model is obtained:
fig. 4 shows an equivalent circuit of the cylindrical four-coil wireless energy transmission system. As shown in fig. 4, the resonant capacitor C 1 And a resonance capacitor C 4 To infinity, i.e
And
both terms are absent. Z 1 -Z 4 Respectively representing the impedances, I, of the 1 st to 4 th loops 1 -I 4 Respectively representing the currents of the 1 st to 4 th loops, L 1 -L 4 Inductances, R, of 1 st to 4 th coils, respectively 1 -R 4 Resistances of 1 st to 4 th coils, C 2 Is the resonance capacitance of the 2 nd coil, C 3 Is the resonant capacitance of the 3 rd coil, M 12 Representing the mutual inductance between the 1 st and 2 nd coils, M 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 Each representing the mutual inductance, V, between the coils to which its numerical index corresponds S Is the supply voltage, R S Is the internal resistance of the power supply.
S5, constructing an objective function and constraint conditions of the cylindrical four-coil wireless energy transmission system;
s5.1, constructing a target function of the cylindrical four-coil wireless energy transmission system;
wherein eta is the output efficiency, P, of the cylindrical four-coil wireless energy transmission system IN Input power, P, for a cylindrical four-coil wireless energy transmission system OUT Output power, V, for a cylindrical four-coil wireless energy transmission system OUT For the output voltage of the cylindrical four-coil wireless energy transmission system, abs (DEG) represents an absolute value, re (DEG) represents a real part, I 1 Is the current in the 1 st loop, I 4 The current in the 4 th loop.
S5.2, establishing constraint conditions of the cylindrical four-coil wireless energy transmission system;
the constraint conditions comprise linear constraint conditions and nonlinear constraint conditions;
wherein the linear constraint condition is:
X(x 1LOW ,x 2LOW ,...,x 21LOW )≤X(x 1 ,x 2 ,...,x 21 )≤X(x 1HIGH ,x 2HIGH ,...,x 21HIGH )
wherein x is 1 ,x 2 ,...,x 21 Represents the parameter to be optimized, x, of the cylindrical four-coil wireless energy transmission system 1LOW ,x 2LOW ,...,x 21LOW Denotes x 1 ,x 2 ,...,x 21 Lower limit value, x, corresponding to each parameter in (1) 1HIGH ,x 2HIGH ,...,x 21HIGH Denotes x 1 ,x 2 ,...,x 21 The upper limit value corresponding to each parameter in (1), and X (·) represents a parameter set;
in the present embodiment, four columns are specifiedFor a coil wireless energy transmission system, the 23 parameters to be optimized are: x is the number of 1 Is the system frequency, x 2 -x 5 Diameter, x, of coil-constituting wires of 1 st to 4 th coils, respectively 6 -x 9 Ca values, x, of the 1 st to 4 th coils, respectively 10 -x 13 Diameter, x, of the 1 st to 4 th coils, respectively 14 -x 17 Number of turns, x, of the 1 st to 4 th coils, respectively 18 Is the distance, x, between the 1 st and 2 nd coils 19 Is the distance, x, between the 2 nd coil and the 3 rd coil 20 Is the distance, x, between the 3 rd coil and the 4 th coil 21 Is a load.
The nonlinear constraints are:
wherein, P LOW And P HIGH Respectively is output power P OUT Lower and upper limits of, V LOW And V HIGH Are respectively an output voltage V OUT Lower and upper limits of.
And S6, writing the model, the objective function and the constraint condition established in the steps S1-S5 into a simulation tool MATLAB, and then iterating the parameters of the multi-coil wireless energy transmission system by calling a genetic algorithm in the MATLAB under the constraint condition by taking the objective function as a target, so as to output the optimized multi-coil wireless energy transmission system.
In the embodiment, the voltage of the direct-current power supply is set to be 48V, the internal resistance of the power supply is 0 omega, the range of the output voltage is set to be 39V-40V, the range of the output power is set to be 99W-101W, simulation is carried out, the maximum efficiency of the system after genetic algorithm optimization is 87.85%, the output power is 100W, the output voltage is 40.08V, and the optimal working frequency is 440kHz. Fig. 5 (a) is a graph of system efficiency versus frequency, output power versus frequency plotted by changing only the frequency under the optimized system optimum parameters, and fig. 5 (b) is a graph of system efficiency versus frequency, output voltage versus frequency plotted by changing only the frequency under the optimized system optimum parameters.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.
Claims (7)
1. A modeling and optimizing method of a multi-coil wireless energy transmission system is characterized by comprising the following steps:
(1) Constructing a self-inductance model of the coil;
(2) Constructing a resistance model of the coil under the consideration of skin effect and proximity effect;
(3) Constructing a mutual inductance model of the coil;
(4) Constructing a multi-coil wireless energy transmission system model;
(5) Constructing an objective function and constraint conditions of the multi-coil wireless energy transmission system;
(6) Writing the model, the objective function and the constraint condition established in the steps (1) - (5) into a simulation tool MATLAB, and then iterating the parameters of the multi-coil wireless energy transmission system by calling a genetic algorithm in the MATLAB under the constraint condition by taking the objective function as a target, thereby outputting the optimized multi-coil wireless energy transmission system.
2. The modeling and optimization method for a multi-coil wireless energy transfer system according to claim 1, wherein the coil is selected from a cylindrical spiral coil or a planar spiral coil;
when the cylindrical spiral coil is selected, the corresponding self-inductance model is as follows:
wherein i represents a coil number, L i Is the self-inductance of the ith coil, r i Radius of the i-th coil, N i Number of turns of i-th coil, l i Is the length of the ith coil, K ni Is the Changon coefficient, k, of the ith coil i And
to calculate the required intermediate variables, K (K) i ) Is k is i Elliptic first complete integration of (c), E (k) i ) Is k is i Second full integration of the ellipse;
when the planar spiral coil is selected, the corresponding self-inductance model is as follows:
wherein L is i Is the self-inductance of the ith coil, a i Denotes the geometric radius, ca, of the ith coil i Is the pitch P of the ith coil i And the diameter of the wire constituting the coil
Ratio of (A) to (B), N i Number of turns of i-th coil, r oi Is the distance from the center reference point of the ith coil to the center of the last turn of the wire, D oi ,D Ii Is an intermediate variable.
3. The method of claim 1, wherein the resistance model of the coil is:
wherein R is i To take into account the resistance of the ith coil under skin and proximity effects, σ is the wire that makes up the coilμ is the vacuum permeability, d i Is the diameter of the i-th coil,
omega is the angular frequency of the multi-coil wireless energy transmission system, R, for the diameter of the wire forming the coil Ti 、R Pi 、R Oi 、R Ki Is an intermediate variable.
4. The modeling and optimization method for the multi-coil wireless energy transmission system according to claim 1, wherein the mutual inductance model of the coil is selected from a mutual inductance model of a cylindrical spiral coil or a mutual inductance model of a planar spiral coil;
wherein, the mutual inductance model of the cylindrical spiral coil is as follows:
wherein M is ij The number of turns of the coil is N i And the number of turns of the coil is N j Of j-th coil, T ij Is the mutual inductance between the ith coil and the single turn coil of the jth coil, r i Radius of the i-th coil, r j Radius of the jth coil, m ij Is an intermediate variable, K (m) ij ) And E (m) ij ) Are respectively related to m ij The first and second elliptical integrals of (a),
is the ith coil
Center of wire of loop and the th of j coil
The distance between the centers of the coil conductors,
has a value in the range of 1-N i ，
Has a value in the range of 1-N j ，offset ij Is the offset between the ith and jth coil, P i ,P j The pitches of the ith coil and the jth coil respectively;
the mutual inductance model of the planar spiral coil is as follows:
wherein M is ij The number of turns of the coil is N i And the number of turns of the coil is N j Mutual inductance between jth coils of (1), T ij Is the mutual inductance between the i-th coil and the single turn coil of the j-th coil, m ij Is an intermediate variable, K (m) ij ) And E (m) ij ) Are respectively related to m ij The first and second elliptical integrals of (a),
is the distance between the ith and jth coil, e 1 Indicating the ith in the ith coil
Distance between the center of the wire of the coil and the central axis of the ith coil, e 2 Denotes the th in the jth coil
Distance between center of coil wire and j central axis of coil, P i ,P j Pitch, r, of the ith and jth coils, respectively i Radius of the ith coil, r j Is the radius of the jth coil,
has a value range of 1-N i ，
Has a value in the range of 1-N j 。
5. The method of claim 1, wherein the multi-coil wireless energy transfer system model is:
wherein n is the number of coils, Z i Representing the impedance, R, of the ith loop in a multi-coil wireless energy transfer system S Is the internal resistance of the power supply, R L Is a load resistance, R i Is the equivalent impedance of the ith coil, L i Inductance of the i-th coil, C i Is the resonant capacitance of the ith coil, I i I =1,2, \ 8230;, n, M, is the current in the ith loop in which the ith coil is located ij Is the mutual inductance between the ith coil and the jth coil, V S Is the supply voltage.
6. The method of claim 1, wherein the objective function of the multi-coil wireless energy transfer system is:
wherein eta is the output efficiency, P, of the multi-coil wireless energy transmission system IN Input power, P, for a multi-coil wireless energy transfer system OUT For the output power, V, of a multi-coil wireless energy transfer system OUT For the output voltage of the multi-coil wireless energy transmission system, abs (·) represents the absolute value, re (·) represents the real part, I 1 Represents the current in the 1 st loop, I n Representing the current in the nth loop.
7. The modeling and optimization method for the multi-coil wireless energy transmission system according to claim 1, wherein the constraints of the multi-coil wireless energy transmission system include linear constraints and non-linear constraints;
wherein the linear constraint condition is:
X(x 1LOW ,x 2LOW ,...,x (5n+1)LOW )≤X(x 1 ,x 2 ,...,x 5n+1 )≤X(x 1HIGH ,x 2HIGH ,...,x (5n+1)HIGH )
wherein x is 1 ,x 2 ,...,x 5n+1 Representing a parameter to be optimized, x, of a multi-coil wireless energy transfer system 1LOW ,x 2LOW ,...,x (5n+1)LOW Represents x 1 ,x 2 ,...,x 5n+1 The lower limit value, x, of each parameter 1HIGH ,x 2HIGH ,...,x (5n+1)HIGH Denotes x 1 ,x 2 ,...,x 5n+1 The upper limit value corresponding to each parameter in (1), and X (·) represents a parameter set;
the nonlinear constraints are:
wherein, P LOW And P HIGH Respectively an output power P OUT Lower and upper limits of, V LOW And V HIGH Are respectively an output voltage V OUT The lower and upper limits of (c).
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