CN112671116A - MCR-WPT system resonance point configuration method based on modal analysis theory - Google Patents

MCR-WPT system resonance point configuration method based on modal analysis theory Download PDF

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CN112671116A
CN112671116A CN202110064582.XA CN202110064582A CN112671116A CN 112671116 A CN112671116 A CN 112671116A CN 202110064582 A CN202110064582 A CN 202110064582A CN 112671116 A CN112671116 A CN 112671116A
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mcr
wpt system
matrix
electrical parameter
resonance
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沈艳霞
赵越
赵芝璞
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Jiangnan University
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Abstract

The invention discloses a method for configuring resonance points of an MCR-WPT system based on a modal analysis theory, which comprises the following steps: judging whether the MCR-WPT system belongs to a first type or not, if so, establishing a modal analysis model of the MCR-WPT system, acquiring an electrical parameter expression and a modal index expression according to the modal analysis model, establishing a corresponding relation between the electrical parameter expression and the modal index expression, and calculating the mutual inductance between the coupling inductance coils; if the MCR-WPT system does not belong to the first type, a fitness function is established, an electrical parameter matrix is established, and the fitness function and the electrical parameter matrix are optimized by adopting a PSO algorithm, so that a feasible solution of the electrical parameter matrix meeting the configuration requirement of the resonance point is obtained. The invention can accurately configure the system resonance point and ensure the tuning effect.

Description

MCR-WPT system resonance point configuration method based on modal analysis theory
Technical Field
The invention relates to the technical field of wireless power transmission, in particular to a method for configuring a resonance point of an MCR-WPT system based on a modal analysis theory.
Background
The MCR-WPT (Magnetically Coupled Resonant Power Transfer) system can meet the requirements of Wireless transmission with large output Power and high efficiency at medium distance, and thus, the system has been industrially applied in the fields of implantable medical devices, electric vehicles, household appliances, and the like.
The MCR-WPT system is essentially a vibration system with multiple degrees of freedom, resonance between coils can be realized only under specific transmission distance and frequency, the system is extremely sensitive to the transmission distance and the frequency, slight change of parameters can cause detuning, sudden drop of system efficacy and sudden increase of output current are caused, in order to keep the system resonant, in the prior art, electric parameters of the system are generally compensated through a control link, such as frequency tracking control, impedance matching and coil coupling strength adjustment, although the control link can enable the MCR-WPT system to resonate again, the output power of the tuned system is difficult to maintain the original level, and the tuning effect is not ideal. The power-frequency characteristics of the MCR-WPT system are jointly determined by a plurality of electrical parameters of the system, the corresponding relation is quite complex, and the modeling theory (circuit theory, coupling mode theory and the like) of the existing MCR-WPT system cannot establish the corresponding relation between power and frequency and the electrical parameters of the system, so that the resonance point of the system cannot be accurately configured, and the tuning effect cannot be guaranteed.
Disclosure of Invention
The invention aims to provide a method for configuring a resonance point of an MCR-WPT system based on a modal analysis theory, which can accurately configure the resonance point of the system and ensure a tuning effect.
In order to solve the technical problems, the technical scheme provided by the invention is as follows:
a resonance point configuration method of an MCR-WPT system based on modal analysis theory comprises the following steps:
1) judging whether the MCR-WPT system belongs to a first type, if so, executing the step 2), otherwise, executing the step 5);
the first type is: the number of the coupled inductance coils is not more than 3, and only the coupling coefficient is variable in the MCR-WPT system;
2) establishing a modal analysis model of the MCR-WPT system, and executing the step 3);
3) acquiring an electrical parameter expression and a modal index expression according to the modal analysis model, establishing a corresponding relation between the electrical parameter expression and the modal index expression, and executing the step 4);
4) calculating the mutual inductance between the coupling inductance coils according to the corresponding relation between the electrical parameter expression and the modal index expression and the expected resonance frequency of the resonance point of the MCR-WPT system;
5) establishing a fitness function according to the expected resonance frequency and the actual resonance frequency of the resonance point of the MCR-WPT system, establishing an electrical parameter matrix, and executing the step 6);
6) and optimizing the fitness function and the electrical parameter matrix by adopting a PSO algorithm so as to obtain a feasible solution of the electrical parameter matrix meeting the configuration requirement of the resonance point.
In one embodiment, the MCR-WPT system comprises a transmitting loop and a receiving loop, wherein a plurality of relay loops are arranged between the transmitting loop and the receiving loop, the transmitting loop, the receiving loop and the relay loops are LC resonant circuits, and each resonant circuit comprises a coupling inductance coil, a tuning capacitor, a resistor and an alternating current power supply which are connected in series.
In one embodiment, the modal analysis model of the MCR-WPT system in step 2) is:
Figure BDA0002903642740000021
wherein S represents a system matrix, L represents an inductance matrix, C represents a capacitance matrix, R represents a resistance matrix, In×nThe unit matrix is represented by a matrix of units,
Figure BDA0002903642740000022
Lirepresenting the inductance value, C, of the coupled inductor in the ith LC resonant circuitiRepresenting the capacitance, R, of the capacitance in the ith LC resonant circuitiRepresents a resistance value, M, in the ith LC resonance circuitijRepresents the mutual inductance value between the coupling inductance coils of the ith LC resonance circuit and the jth LC resonance circuit, i ═ 1,2 …, n],j＝[1,2…,n]And n is the number of LC resonant circuits.
In one embodiment, theThe system matrix S has n pairs of conjugate eigenvalues, and the real parts of the n pairs of conjugate eigenvalues are defined to be alphanAll the modulus values are | λnIf the imaginary part is + -beta respectivelynThen the nth pair of eigenvalues of the system matrix S is λn＝-αn+jβn，
Figure BDA0002903642740000031
Characteristic value lambdan、
Figure BDA0002903642740000032
Of the mode (d) and the resonance frequency f of the nth resonance pointnSatisfies the following conditions:
Figure BDA0002903642740000033
the characteristic equation of the system matrix S is converted into the following modal index expression F1(lambda) and the electrical parameter expression F2(λ)：
F1(λ)＝λ2n+z2n-1(αn,λn,…，α1,λ1)λ2n-1+z2n-2(αn,λn,…，α1,λ1)λ2n-2+…+z0(αn,λn,…，α1,λ1)；
F2(λ)＝λ2n+g2n-1(L,C,R)λ2n-1+g2n-2(L,C,R)λ2n-2+…+g0(L,C,R)＝0
Wherein z is2n-t(αn,λn,…，α1,λ1) Representing a modal function, g2n-t(L, C, R) each represents an electrical parameter function, t ═ 1,2 …,2n](ii) a λ represents a variable of the eigenequation of the system matrix S.
In one embodiment, the correspondence between the electrical parameter expression and the modal index expression is:
Figure BDA0002903642740000034
in one embodiment, the fitness function fitness in step 5) is:
fitness＝-(W1(f1expected-f)2+…+Wn(fn expected-fn)2)；
wherein f isi expectedRepresenting the ith desired resonance frequency, fiDenotes the ith actual resonance frequency, WiDenotes the ith error weight, i ═ 1,2 …, n]And n is the number of LC resonant circuits.
The invention has the following beneficial effects: the method for configuring the resonance points of the MCR-WPT system based on the modal analysis theory can accurately configure the resonance points of different types of MCR-WPT systems, is simple and convenient, has strong universality, and effectively ensures the tuning effect.
Drawings
FIG. 1 is a circuit diagram of an MCR-WPT system of the present invention;
FIG. 2 is a circuit diagram of a dual coil MCR-WPT system;
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
The embodiment discloses a resonance point configuration method of an MCR-WPT system based on a modal analysis theory, which comprises the following steps:
1) judging whether the MCR-WPT system belongs to a first type, if so, executing the step 2), otherwise, executing the step 5);
the first type is: the number n of the coupling inductance coils is less than or equal to 3, and only the coupling coefficient is variable in the MCR-WPT system;
it is understood that MCR-WPT systems not belonging to the first type are systems that limit partial or no electrical parameters, for example multi-coil (number of coupled inductors n > 3) MCR-WPT systems or few-coil (number of coupled inductors n ≦ 3) MCR-WPT systems that do not limit electrical parameters; the electrical parameters comprise capacitance, inductance, resistance and the number of coupling inductance coils;
2) establishing a modal analysis model of the MCR-WPT system, and executing the step 3);
3) acquiring an electrical parameter expression and a modal index expression according to the modal analysis model, establishing a corresponding relation between the electrical parameter expression and the modal index expression, and executing the step 4);
4) calculating the mutual inductance between the coupling inductance coils according to the corresponding relation between the electrical parameter expression and the modal index expression and the expected resonance frequency of the resonance point of the MCR-WPT system;
5) establishing a fitness function according to the expected resonance frequency and the actual resonance frequency of the resonance point of the MCR-WPT system, establishing an electrical parameter matrix, and executing the step 6);
6) and optimizing the fitness function and the electrical parameter matrix by adopting a Particle Swarm Optimization (PSO) algorithm, so as to obtain a feasible solution of the electrical parameter matrix meeting the configuration requirement of the resonance point, thereby completing the system configuration.
The resonance point is an equivalent point where resonance occurs, and the frequency of the resonance point is the resonance frequency.
In one embodiment, as shown in fig. 1, the MCR-WPT system includes a transmitting loop and a receiving loop, wherein a plurality of relay loops are disposed between the transmitting loop and the receiving loop, the transmitting loop, the receiving loop and the relay loops are all LC resonant circuits, and each resonant circuit includes a coupling inductance coil, a tuning capacitor, a resistor and an ac power source connected in series. For example, in fig. 1, n LC resonant circuits are included, the leftmost LC resonant circuit may be a transmitting circuit, the rightmost LC resonant circuit may be a receiving circuit, and a plurality of LC resonant circuits between the transmitting circuit and the receiving circuit may form a plurality of relay circuits.
In one embodiment, the modal analysis model of the MCR-WPT system in step 2) is:
Figure BDA0002903642740000051
whereinS denotes a system matrix, L denotes an inductance matrix, C denotes a capacitance matrix, R denotes a resistance matrix, In×nThe unit matrix is represented by a matrix of units,
Figure BDA0002903642740000052
Lirepresenting the inductance value, C, of the coupled inductor in the ith LC resonant circuitiRepresenting the capacitance, R, of the capacitance in the ith LC resonant circuitiRepresents a resistance value, M, in the ith LC resonance circuitijRepresents the mutual inductance value between the coupling inductance coils of the ith LC resonance circuit and the jth LC resonance circuit, i ═ 1,2 …, n],j＝[1,2…,n]And n is the number of LC resonant circuits, namely the number of coupled inductors. For example, L1Representing the inductance, C, of the coupled inductor in the 1 st LC resonant circuit1Representing the capacitance, R, of the capacitor in the 1 st LC resonance circuit1Represents the resistance value, M, in the 1 st LC resonance circuit12Representing the mutual inductance between the coupled inductors of the 1 st LC tank and the 2 nd LC tank.
Further, the system matrix S has n pairs of conjugate eigenvalues, and the real parts of the n pairs of conjugate eigenvalues are defined to be-alphanAll the modulus values are | λnIf the imaginary part is + -beta respectivelynIf the n-th pair of eigenvalues of the system matrix S is λn＝-αn+jβn，
Figure BDA0002903642740000053
Characteristic value lambdan、
Figure BDA0002903642740000054
Of the mode (d) and the resonance frequency f of the nth resonance pointnSatisfies the following conditions:
Figure BDA0002903642740000055
the eigen equation of the system matrix S can be converted into the following two expressions: modal index expression F1(lambda) and the electrical parameter expression F2(λ)：
The modal index expression is:
F1(λ)＝λ2n+z2n-1(αn,λn,…，α1,λ1)λ2n-1+z2n-2(αn,λn,…，α1,λ1)λ2n-2+…+z0(αn,λn,…，α1,λ1)；
the electrical parameter expression is:
F2(λ)＝λ2n+g2n-1(L,C,R)λ2n-1+g2n-2(L,C,R)λ2n-2+…+g0(L,C,R)＝0
wherein z is2n-t(αn,λn,…，α1,λ1) Representing a modal function, g2n-t(L, C, R) each represents an electrical parameter function, t ═ 1,2 …,2n](ii) a λ represents a variable of the eigenequation of the system matrix S.
Wherein the electrical parameter expression is represented by
Figure BDA0002903642740000061
To obtain the compound of the formula In×nAnd I2n×2nEach represents an identity matrix.
Further, the comparison between the terms of the electrical parameter expression and the modal index expression can obtain the corresponding relationship between the two expressions, and the corresponding relationship is 2n linearly independent equations formed by the resonance points and the electrical parameters:
Figure BDA0002903642740000062
in one embodiment, the fitness function fitness in step 5) is:
fitness＝-(W1(f1expected-f)2+…+Wn(fn expected-fn)2)；
wherein f isi expectedRepresenting the ith desired resonance frequency, fiDenotes the ith actual resonance frequency, WiDenotes the ith error weight for error normalization, i ═ 1,2 …, n]And n is the number of LC resonant circuits, namely the number of coupled inductors.
The method for configuring the resonant point of the MCR-WPT system is specifically described below by taking a dual-coil MCR-WPT system (as shown in fig. 2), that is, an MCR-WPT system with 2 coupled inductors as an example:
the electrical parameters of the double-coil MCR-WPT system comprise an alternating voltage v1Inductance L1,L2Capacitor C1,C2Resistance R1,R2Etc.;
AC voltage input constitution vector v ═ v of double-coil MCR-WPT system1,0]Desired resonant frequency of f1 expectedOr f2 expected(resonance point arrangement target) with an actual resonance frequency f1,f2Then, there are:
Figure BDA0002903642740000071
wherein the content of the first and second substances,
Figure BDA0002903642740000072
the system matrix S has 2 pairs of conjugate eigenvalues, then:
Figure BDA0002903642740000073
Figure BDA0002903642740000074
so as to obtain the corresponding relation equation between the electrical parameter expression and the modal index expression as follows:
Figure BDA0002903642740000075
when the dual coil MCR-WPT system is of the first type, i.e., the coupling coefficient variable only type, the system parameter setting conditions are as shown in table 1. Validating a configuration target f1 expectedIn which case only one variable of the electrical parameter, i.e. the mutual inductance M, is present12The eigenvalues of the system matrix S have 4 variables: alpha is alpha1,λ1,α2,λ2According to f1 expected1 variable lambda which can solve the eigenvalues1＝2πf1 expectedSubstituting into formula (1) to obtain M12The coupling coefficient k is further obtained through the analytical solution, the specific configuration result is shown in table 2, the "experimental value" in the table is obtained through field experiments, the "simulation value" is obtained through the matlab simulation model, and the "calculated value" is obtained through the calculation of the method in the embodiment.
TABLE 1 parameter setting table for double-coil MCR-WPT system
Figure BDA0002903642740000076
Figure BDA0002903642740000081
TABLE 2 configuration target Table for a first type of dual-coil MCR-WPT System
Figure BDA0002903642740000082
As can be seen from the results in table 2, for the dual-coil MCR-WPT system with only variable coupling coefficient, the calculated value of the resonance point configured by the method of the present embodiment can be well matched with the simulation value. f. of1、f2The experimental value is obtained by an observation method, and the difference between the experimental value and the simulated value is not large.
When the double-coil MCR-WPT system does not belong to the first type but belongs to a type without limiting the electrical parameters, confirming the configuration target f1 expected，f2 expectedAll inductance values in the electrical parameter matrix L, C, R are selected,The mutual inductance value, the resistance value and the capacitance value are used as variables to be optimized, and the fitness function is (W)1(f1 expected-f)2+W2(f2 expected-f2)2) Then, a PSO algorithm is adopted to optimize the fitness function and the variable to be optimized, so that a feasible solution of the electrical parameter matrix L, C, R capable of meeting the configuration requirement of the resonance point can be given, and the specific configuration result is shown in Table 3.
TABLE 3 Dual-coil MCR-WPT System configuration target Table without limiting Electrical parameters
Figure BDA0002903642740000083
From the results in table 3, it can be seen that for a dual-coil MCR-WPT system without limiting the electrical parameters, the system can be configured at any resonance point and a feasible solution for all electrical parameters can be obtained. It is noted with respect to table 3 that in configuring an MCR-WPT system without limiting electrical parameters, the resonant frequency (f) is determined according to the desired resonant frequency (f)1 expected，f2 expected) The error weights W1 and W2 are selected to be appropriate, so that f is1、f2Are evenly distributed around the corresponding desired values. For Example, in Table 3, resonance point f in sample 1-21、f2The expected values of (A) are 25kHz and 50kHz, while the resonance point f in sample 3-4 is1、f2Desired values of 35kHz and 55kHz, in order to compensate for f1So that f is properly reduced in the Example 3-41So that f is reduced without any imbalance1、f2Error from the corresponding expected value.
In the method for configuring the resonance point of the MCR-WPT system based on the modal analysis theory according to the embodiment, for the MCR-WPT system with few coils, which is only coupled and variable (the number n of coupled inductor coils is less than or equal to 3), that is, for the first type of MCR-WPT system, including the MCR-WPT system with single transmission, single reception, single transmission, double reception, and double transmission, single reception, the coupling coefficient value or the mutual inductance value required for configuring the resonance point can be rapidly and accurately calculated; for other MCR-WPT systems except the first type, the MCR-WPT system can be configured at any resonance point, and feasible solutions of all electrical parameters required by configuration are given, including all inductance, mutual inductance, capacitance and resistance, so that the flexibility of configuration of the resonance point of the MCR-WPT system is improved. When the MCR-WPT system without limiting the electrical parameters is designed, other indexes such as transmission efficiency and output power can be added into the fitness function of the algorithm to serve as a part of the optimization target of the algorithm, so that the requirements of system design on power and efficiency are met, and the method has high universality and expansibility.
In summary, the resonance point configuration method of the MCR-WPT system based on the modal analysis theory according to the embodiment can configure the MCR-WPT system with only variable coupling few coils (the number n of coupling inductors is less than or equal to 3) at the target resonance point, and provide an analytic solution of the coupling coefficient; the MCR-WPT system with unlimited electrical parameters or limited partial electrical parameters can be configured at any resonance point, feasible solutions of all the electrical parameters are provided, the configuration method is simple and convenient, the universality is strong, the configuration is accurate, the system can output required power under the selected frequency and transmission distance, the transmission is stable, and the tuning effect is effectively ensured.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.

Claims (6)

1. A resonance point configuration method of an MCR-WPT system based on a modal analysis theory is characterized by comprising the following steps:
1) judging whether the MCR-WPT system belongs to a first type, if so, executing the step 2), otherwise, executing the step 5);
the first type is: the number of the coupled inductance coils is not more than 3, and only the coupling coefficient is variable in the MCR-WPT system;
2) establishing a modal analysis model of the MCR-WPT system, and executing the step 3);
3) acquiring an electrical parameter expression and a modal index expression according to the modal analysis model, establishing a corresponding relation between the electrical parameter expression and the modal index expression, and executing the step 4);
4) calculating the mutual inductance between the coupling inductance coils according to the corresponding relation between the electrical parameter expression and the modal index expression and the expected resonance frequency of the resonance point of the MCR-WPT system;
5) establishing a fitness function according to the expected resonance frequency and the actual resonance frequency of the resonance point of the MCR-WPT system, establishing an electrical parameter matrix, and executing the step 6);
6) and optimizing the fitness function and the electrical parameter matrix by adopting a PSO algorithm so as to obtain a feasible solution of the electrical parameter matrix meeting the configuration requirement of the resonance point.
2. The mode analysis theory-based MCR-WPT system resonance point configuration method according to claim 1, wherein the MCR-WPT system comprises a transmitting loop and a receiving loop, a plurality of relay loops are arranged between the transmitting loop and the receiving loop, the transmitting loop, the receiving loop and the relay loops are LC resonance circuits, and the resonance circuits comprise a coupling inductance coil, a tuning capacitor, a resistor and an alternating current power supply which are connected in series.
3. The resonance point configuration method of the MCR-WPT system based on the modal analysis theory according to claim 2, wherein the modal analysis model of the MCR-WPT system in the step 2) is:
Figure FDA0002903642730000011
wherein S represents a system matrix, L represents an inductance matrix, C represents a capacitance matrix, R represents a resistance matrix, In×nThe unit matrix is represented by a matrix of units,
Figure FDA0002903642730000021
Lirepresenting the inductance value, C, of the coupled inductor in the ith LC resonant circuitiRepresenting the capacitance, R, of the capacitance in the ith LC resonant circuitiRepresents a resistance value, M, in the ith LC resonance circuitijRepresents the mutual inductance value between the coupling inductance coils of the ith LC resonance circuit and the jth LC resonance circuit, i ═ 1,2 …, n],j＝[1,2…,n]And n is the number of LC resonant circuits.
4. The mode analysis theory-based MCR-WPT system resonance point configuration method according to claim 3, wherein the system matrix S has n pairs of conjugate eigenvalues, and the real part of the n pair of conjugate eigenvalues is defined to be- αnAll the modulus values are | λnIf the imaginary part is + -beta respectivelynThen the nth pair of eigenvalues of the system matrix S is λn＝-αn+jβn，
Figure FDA0002903642730000022
Characteristic value lambdan、
Figure FDA0002903642730000023
Of the mode (d) and the resonance frequency f of the nth resonance pointnSatisfies the following conditions:
Figure FDA0002903642730000024
the characteristic equation of the system matrix S is converted into the following modal index expression F1(lambda) and the electrical parameter expression F2(λ)：
F1(λ)＝λ2n+z2n-1(αn,λn,…，α1,λ1)λ2n-1+z2n-2(αn,λn,…，α1,λ1)λ2n-2+…+z0(αn，λn，…，α1，λ1)；
F2(λ)＝λ2n+g2n-1(L,C,R)λ2n-1+g2n-2(L,C,R)λ2n-2+…+g0(L,C,R)＝0
Wherein z is2n-t(αn,λn,…，α1,λ1) Representing a modal function, g2n-t(L, C, R) each represents an electrical parameter function, t ═ 1,2 …,2n](ii) a λ represents a variable of the eigenequation of the system matrix S.
5. The mode analysis theory-based MCR-WPT system resonance point configuration method according to claim 4, wherein the correspondence between the electrical parameter expression and the mode index expression is as follows:
Figure FDA0002903642730000025
6. the method for configuring the resonance point of the MCR-WPT system based on the modal analysis theory as claimed in claim 1, wherein the fitness function fitness in the step 5) is:
fitness＝-(W1(f1expected-f)2+…+Wn(fnexpected-fn)2)；
wherein f isiexpectedRepresenting the ith desired resonance frequency, fiDenotes the ith actual resonance frequency, WiDenotes the ith error weight, i ═ 1,2 …, n]And n is the number of LC resonant circuits.
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