CN109067009B - MC-WPT system design method based on center frequency and bandwidth - Google Patents

Abstract

The invention discloses a MC-WPT system design method based on center frequency and bandwidth, which is characterized in that mutual inductance parameters, capacitance parameters and resistance parameters in the MC-WPT system are configured through the center frequency and the bandwidth, and a multi-band MC-WPT system can be obtained without adding any extra LC circuit or coil.

Description

MC-WPT system design method based on center frequency and bandwidth

Technical Field

The invention relates to the technical field of MC-WPT (Magnetic coupling wireless power transfer), in particular to a MC-WPT system design method based on center frequency and bandwidth.

Background

The MC-WPT technology realizes the transmission of electric energy from a power supply side to a consumer side without electrical connection. Due to the electrical isolation of the power supply end and the load end, the technology has the advantages of safety, reliability, flexibility and the like, and is widely applied to the fields of household appliances, biomedicine, electric vehicles and the like at present. With the development and application popularization of the MC-WPT technology, independent and mutually incompatible wireless charging frequency band standards are proposed by a plurality of industry associations at present. Driven by this demand, the MC-WPT technology is currently being extensively studied by researchers at home and abroad. In addition, MC-WPT systems are also of interest because they can be used for signal energy co-transmission.

At present, when designing an MC-WPT system, in order to obtain multiple frequency bands, an additional LC branch circuit or an additional coil is usually required, which increases additional cross coupling, and the number of LC branch circuits or the number of additional coils must increase with the increase of the number of frequency bands, so the conventional design method complicates the system structure. Since the traditional MC-WPT system design method is based on circuit analysis, the system analysis design with complex circuit structure becomes extremely difficult and is not applicable. Therefore, the conventional design method is usually only suitable for the MC-WPT system with a small number of frequency bands and a simple structure, but not suitable for the multi-coil structure system with a large number of frequency bands or a complex structure.

Disclosure of Invention

In order to solve the above technical problem, the present invention provides a MC-WPT system design method based on center frequency and bandwidth, including:

s11: inductance matrix L of MC-WPT system_n×nCapacitor matrix C_n×nAnd a resistance matrix R_n×nSubstituting into the actual characteristic equation lambda of the MC-WPT system²[LC]+λ[RC]+I_n×n1 | ═ 0, give

f(λ)_actual＝λ²ⁿ+d_2n-1λ^2n-1+d_2n-2λ^2n-2…d₁λ+d₀； (1)

The inductance matrix comprises mutual inductance parameters to be determined, the capacitance matrix comprises capacitance parameters to be determined, and the resistance matrix comprises resistance parameters to be determined;

s12: according to the frequency band number k and the central frequency f which need to be met by the MC-WPT system_0,1,f_0,2…f_0,kAnd bandwidths b corresponding to the respective center frequencies₁,b₂…b_kDetermining a desired eigenvalue to meet the performance requirement

Wherein, w_0,q＝2πf_0,q,B_q＝2πb_q,

r_qThe number of the q frequency band is the weight number;

s13, obtaining the expected characteristic equation of the MC-WPT system according to the obtained expected characteristic value as

S14, determining mutual inductance parameters, capacitance parameters and resistance parameters of the MC-WPT system according to the formula (1) and the formula (2);

the n, the q and the k are positive integers, the n is the number of circuits of the MC-WPT system, each circuit comprises a coil, and the k is less than or equal to n.

Further, the air conditioner is provided with a fan,

L_mis the coil self-inductance of the mth circuit, R_mIs the resistance of the mth circuit, C_mIs a compensation capacitor of the mth circuit, M_mjFor the mutual inductance between the coil in the mth circuit and the coil in the jth circuit, m is 1,2, … n, and j is 1,2, … n.

Further, said R_mIs the sum of the coil internal resistance and the load resistance of the mth circuit.

The MC-WPT system design method based on the center frequency and the bandwidth, provided by the invention, can be used for configuring the mutual inductance parameter, the capacitance parameter and the resistance parameter in the MC-WPT system through the center frequency and the bandwidth without adding any extra LC circuit or coil to obtain the needed MC-WPT system.

Drawings

The invention will be further described with reference to the accompanying drawings and examples, in which:

fig. 1 is a schematic flow chart of a MC-WPT system design method based on center frequency and bandwidth according to an embodiment of the present invention;

fig. 2 is a schematic equivalent circuit diagram of an MC-WPT system according to an embodiment of the present invention;

FIG. 3 is a drawing of I provided by an embodiment of the present invention_q,mA curve graph of | variation with power supply frequency ω;

fig. 4 is a schematic diagram of simulated and actually measured output power of a single-frequency band system in an example according to an embodiment of the present invention;

fig. 5 is a schematic diagram of simulated and actually measured output power of an exemplary dual-band system according to an embodiment of the present invention.

Detailed Description

It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

The present embodiment provides a MC-WPT system design method based on center frequency and bandwidth, please refer to fig. 1, which includes:

s11: inductance matrix L of MC-WPT system_n×nCapacitor matrix C_n×nAnd a resistance matrix R_n×nSubstituting into the actual characteristic equation | λ of the system²[LC]+λ[RC]+I_n×n1 | ═ 0, give

f(λ)_actual＝λ²ⁿ+d_2n-1λ^2n-1+d_2n-2λ^2n-2…d₁λ+d₀； (1)

The inductance matrix comprises mutual inductance parameters to be determined, the capacitance matrix comprises capacitance parameters to be determined, and the resistance matrix comprises resistance parameters to be determined; in this embodiment, the process of determining the mutual inductance parameter, the capacitance parameter, and the resistance parameter is also the process of designing the MC-WPT system.

In this example, L is_n×n、C_n×n、R_n×nAre respectively expressed as n × n matrix, and L, R, C in the characteristic equation is L_n×n、C_n×n、R_n×n。

In this embodiment, n is the number of circuits of the MC-WPT system, each circuit includes at least one coil, and preferably, each circuit further includes a capacitor, a resistor, and an inductor, at least a part of elements in an inductance matrix of the MC-WPT system in this embodiment are mutual inductance parameters generated based on the inductors in the n circuits, while at least a part of elements in a capacitance matrix in this embodiment are capacitors of the n circuits, at least a part of elements in a resistance matrix in this embodiment are resistors of the n circuits, and at least a part of elements mentioned herein may be preferably n elements in an n × n matrix.

S12: according to the frequency band number k and the central frequency f which need to be satisfied by the MC-WPT system_0,1,f_0,2…f_0,kAnd bandwidths b corresponding to the respective center frequencies₁,b₂…b_kDetermining a desired eigenvalue to meet the performance requirement

And

wherein, w_0,q＝2πf_0,q,B_q＝2πb_q,

r_qIs the weight number of the q-th frequency band.

The MC-WPT system needs to meet the frequency band number k and the center frequency f_0,1,f_0,2…f_0,kAnd bandwidths b corresponding to the respective center frequencies₁,b₂…b_kThe method can be determined by a designer according to an application scene. And the number of weight r of each desired characteristic value_qThe determination can be carried out by the designer or according to a preset algorithm as long as the requirements are met

And (4) finishing.

It should be noted that, the steps S11 and S12 in this embodiment are not in an absolute order, and in some embodiments, the actual characteristic equation may be calculated after the desired characteristic equation is obtained.

S13, obtaining the expected characteristic equation of the MC-WPT system according to the obtained expected characteristic value

And S14, determining the mutual inductance parameter, the capacitance parameter and the resistance parameter of the MC-WPT system according to the formula (1) and the formula (2).

In the embodiment, n, q and k are positive integers, and k is less than or equal to n.

In the embodiment, as shown in fig. 2, the equivalent circuit of the MC-WPT system includes a power supply, a coil self-inductance, a resistor, and a compensation capacitor, and there is mutual inductance between the circuits, where the resistor includes a coil internal resistance and a load resistance, R in fig. 2_pmIs the coil internal resistance of the mth circuit, L_mIs the coil self-inductance of the mth circuit, C_mIs a compensation capacitor of the mth circuit_mIs the voltage across the compensation capacitor of the mth circuit, M_mjIs the mutual inductance between coil m in the mth circuit and coil j in the jth circuit, i_mIs the current of the m-th circuit, R_LmIs the load of the mth circuit; v. of_mIs the power supply of the mth circuit, and n is the number of the circuits; v. of_mAnd R_LmCannot coexist when v_mNot equal to 0 and R_LmWhen it is 0, the circuit m is a transmitting circuit, otherwise V_mR is 0_LmNot equal to 0, the circuit m is a receiving circuit, and when both are 0, the circuit m is a relay circuit.

Based on kirchhoff's voltage law, a mathematical model of the system can be established as

Wherein R is_m＝R_pm+R_LmI.e. the resistance of the mth circuit;

definition vector v ═ v₁v₂… v_n]^T，i＝[i₁i₂… i_n]^TAnd u ═ u₁u₂… u_n]^TThe power supply voltage vector, the current vector and the capacitance voltage vector of the system are respectively. The matrixes L, C and R are respectively an inductance matrix, a capacitance matrix and a resistance matrix of the system, and the expressions are respectively:

order to

And v_in＝[v^T0_1×n]^TRespectively, the state vector and the input vector of the system, the state space model of the system can be established as follows:

wherein:

wherein I_n×nAnd 0_n×nThe state space model shown in equation (5) is normalized and transformed to obtain:

wherein S is a system matrix of the system:

the MC-WPT system with the N coil structures can generate N frequency bands at most. If the number of the frequency bands is less than the number of the coils, the system is indicated to have the frequency band overlapping phenomenon. In general, in a practical system, even if the center frequencies of two frequency bands are very close to each other, the peak heights and the peak widths of the two frequency bands are difficult to be identical at the same time, i.e., the two frequency bands do not completely coincide with each other. This phenomenon indicates that it is difficult for the actual physical system matrix S to have two identical eigenvalues at the same time, i.e. the system matrix S can be diagonalized. When the frequency bands overlap but do not overlap, the spectral parameters of the overlapped frequency bands, including the center frequency and the bandwidth, are difficult to determine. For the convenience of analysis and design, in the present invention, the overlapped frequency bands are designed to be completely overlapped, that is, the system matrix S has completely the same eigenvalue. At this time, based on matrix theory, the system matrix S can not be diagonalized any more, but only approximately normalized.

Suppose there are k (k ≦ n) different eigenvalues of the system matrix S, labeled λ₁,λ₂,…λ_k. Characteristic value lambda_qHas a multiple number of r_q(q is 1,2, … k), then

Since the real eigenvalue components of the eigenvalue matrix of an actual physical system are usually negative real numbers with small absolute values, the eigenvalue λ_qAnd

may be respectively represented as lambda_q＝-α_q+jω_qAnd

α therein_qAnd ω_qIs positive and real and α_qAnd are typically small.

In this case, based on the matrix theory, there are two non-singular matrices

And

so that S phi is phi Λ, operator diag]Indicating that the diagonal matrix is generated with the element in parentheses as the diagonal element, Λ_qAnd

are conjugate matrices of each other, of which Λ_qIs an approximation matrix as shown in equation (9).

From S Φ — Φ Λ, the state space model shown in equation (5) can be expressed as:

wherein y is Φ^-1x，v'＝Φ^-1A^-1v_in. According to

And current vector i and capacitor voltage

In relation to (2)

The current response of the mth circuit loop can be expressed as:

i_m＝Im(I_me^j(ωt+π/2)) (11)

wherein the content of the first and second substances,

wherein the operator Im () represents an imaginary part of the variable,

R_mqis a plurality as shown in formula (13), wherein j_q＝r₁+r₂+…+r_q-1+1。

Based on the formula (11), the current i_mIs equal to the complex number I_mModulo of, i.e. | i_m|＝|I_mL. From the formula (12), a plurality I_mIs composed of k vectors I_q,m(q is 1,2, … k) are superimposed. Obtainable from formula (12) to obtain I_q,mThe mold (A) is as follows:

when the power frequency omega equals omega_q(ω＝Ω_q) When, | I_q,mTaking the maximum value I_q,mmax。

Due to α_qIs usually small, therefore I_q,m|_maxIt will be very large. Furthermore, since the overlapping frequency bands are designed to be completely overlapping, the non-overlapping frequency bands are separated from each other, i.e. k unequal characteristic values λ₁,λ₂,…λ_k(Ω₁,Ω₂,…Ω_k) Are separated from each other, so that when the power supply frequency ω is equal to Ω_qWhen, | I_q,mWill be much larger than the other term | I_j,m(j ≠ q) 1,2, …, k. At this time, I_mCan be regarded as:

the analysis shows that the system has k frequency bands, and the corresponding center frequencies are respectively omega₁,Ω₂,…,Ω_k。I_mThe q frequency band can be expressed as myopia

From the formula (14) | I_q,mThe variation of | with the power supply frequency is a unimodal curve, as shown in fig. 3.

Two points a and b in fig. 3 are half-power points of the q-th frequency band (the difference between the frequencies corresponding to the two half-power points is also the bandwidth mentioned in this embodiment), that is:

the simultaneous solution of equations (12), (15) and (17) can be obtained:

therefore, the bandwidth corresponding to the angular frequency of the q-th frequency band can be calculated as:

based on the above analysis, if there are k characteristic roots λ far away from each other in the system_q＝-α_q+jω_q(q ═ 1, 2.. k), there are k bandwidths in the system, and the corresponding central angular frequency and the bandwidth corresponding to the angular frequency are:

from the above analysis, it can be seen that the number of system bands and the corresponding center frequency and bandwidth are completely determined by the characteristic values of the system. Conversely, based on the desired center frequency and bandwidth of the system, a set of desired eigenvalues can be determined that meet the performance criteria.

Suppose that an MC-WPT system requires k frequency bands (k is less than or equal to n) according to actual requirements, and the specified center frequency and bandwidth are respectively: f. of_0,1,f_0,2…f_0,kAnd b₁,b₂…b_k,. According to the analysis, k frequency bands indicate that k different characteristic values (lambda) exist in the system matrix S₁,λ₂,…λ_k). Characteristic value lambda_qMultiple number of (r)_qCan be determined by the designer and only needs to satisfy

And (4) finishing. Using the formula (20) and a given performance index f_0,1,f_0,2…f_0,kAnd b₁,b₂…b_kAnd w_0,q＝2πf_0,q，B_q＝2πb_qThe expected characteristic values are:

by using the formula (21), a set of characteristic values satisfying a given performance index parameter can be obtained quickly. Then only the system parameters need be determined to make the eigenvalues of the system equal to the designed eigenvalues.

K eigenvalues λ calculated according to equation (21)₁,λ₂,…λ_kThe expected system characteristic equation can be obtained:

furthermore, from the definition of the eigenvalues, it is possible to obtain:

|S-λI_n×n|＝0 (23)

substitution of formula (8) into formula (23) can yield:

equation (24) can be transformed into:

|λ²[LC]+λ[RC]+I_n×n|＝0 (25)

substituting the inductance matrix L, the capacitance matrix C and the resistance matrix R into the formula (26), the characteristic equation of the practical system can be obtained as follows:

f(λ)_actual＝λ²ⁿ+d_2n-1λ^2n-1+d_2n-2λ^2n-2…d₁λ+d₀； (26)

comparing equation (22) and equation (26) yields:

therefore, system parameters meeting performance indexes can be obtained, and the system parameters specifically comprise mutual inductance parameters, capacitance parameters and resistance parameters.

In order to verify the correctness of the method of the present invention, the two-coil structure system is designed and tested by using the above design method, in the embodiment, the two-coil structure includes two circuits, and each circuit includes one coil. Based on the above analysis, the two-coil structure system can be designed as a single-band system or a dual-band system. The procedure is exactly the same for both single band and dual band systems, except that the expected eigenvalues are different.

Supposing that the expected eigenvalue of the system matrix obtained by calculation according to the actual performance requirement is lambda₁＝-α₁+jω₁,

λ₂＝-α₂+jω₂And

substituting the desired characteristic value into equation (22) can obtain the system desired characteristic equation as:

wherein the content of the first and second substances,

furthermore, the inductance matrix L, the capacitance matrix C and the resistance matrix R of the two-coil structural system can be represented as:

substituting equation (30) into | λ²[LC]+λ[RC]+I_n×nThe actual characteristic equation of the two-coil structure system is given as:

comparing equation (28) and equation (31) yields:

in a real system, self-inductance L₁And L₂And corresponding R_p1And R_p2All depend on the actual coil, therefore, L1, L2, R_p1 and R _p2 are determined and known, and from equation (32), C in the capacitance matrix is determined₁And C₂M in an inductor matrix, and R in a resistor matrix₁And R₂Optionally, such that C₁、C₂M and R_LCan also be determined.

The validity of the method provided by the invention is verified by combining specific examples.

Example one:

the center frequency and the bandwidth of an MC-WPT system expected to be designed are determined to be f according to actual needs_o,1150kHz and b₁Assuming that the MC-WPT system has two circuits, each of which includes a coil, and assuming that a one-band system is desired to be designed, it indicates that the one-band system is desired to be designed to satisfy k 1 and r ₁2, then according to formula

The desired characteristic values can be obtained:

wherein λ is₁＝-α₁+jω₁,

In this example, assume that the coil self-inductance L₁And L₂All are 52 mu H, coil internal resistance R_p1And R_p2Are both 0.1 Ω, and C can be determined by substituting these parameters and the formula (33) into the formula (32)₁,C₂,M、R₁And R₂Due to internal resistance R of the coil_p1And R_p2It is known that the corresponding load resistance R can also be determined_L. Detailed description of the inventionThe obtained formula (34):

and carrying out simulation and physical verification by using the determined parameters, wherein the output power variation curve of the simulation and actual measurement system along with the power supply frequency is shown in figure 4. In fig. 4, the abscissa is the power frequency, the ordinate is the output power, the curve is the simulation result, "×" is the actual measurement result, as shown in fig. 4, the system only has one frequency band, the center frequency is 150kHz, the bandwidth is 10kHz, and the desired performance index parameter is completely satisfied.

Example two:

assuming that the center frequencies expected to be designed are respectively f_o,1＝100kHz,f_o,2200kHz, corresponding bandwidth b₁10kHz and b₂At 40kHz, the MC-WPT system is assumed to be a system consisting of two circuits, each of which includes a coil, and it is assumed that a dual-band system is desired to be designed, which indicates that the system has two unequal characteristic values, i.e., k is 2 and r₁＝r₂1, then according to formula

The desired characteristic values can be obtained:

wherein λ is₁＝-α₁+jω₁,

λ₂＝-a₀+jω₂，

In this example, assume that the coil self-inductance L₁And L₂All are 52 mu H, coil internal resistance R_p1And R_p2Are all 0.1 omega, these parameters are compared with the formula (A)35) When the parameters are substituted into the formula (32), the parameter C is determined₁,C₂M and R_LIt can be determined as:

the parameters determined by the formula (36) are used for simulation and physical verification, and the curves of the simulated and actually measured output power changing with the power supply frequency are shown in fig. 5. In fig. 5, the abscissa is the power supply frequency, the ordinate is the output power, the curve is the simulation result, "×" is the actual measurement result, as shown in fig. 5, the system has two frequency bands, the center frequencies are 100kHz and 198kHz respectively, and the bandwidths are 10kHz and 40kHz respectively, which satisfy the expected performance index parameters.

It is to be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.

The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.

Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better implementation manner. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which is stored in a storage medium (such as ROM/RAM, magnetic disk, optical disk) and includes instructions for enabling a terminal (such as a mobile phone, a computer, a server, an air conditioner, or a network device) to execute the method according to the embodiments of the present invention.

While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (2)

1. A method for designing a magnetic coupling wireless power transmission system based on center frequency and bandwidth is characterized by comprising the following steps:

s11, substituting the n × n-dimensional inductance matrix L, the capacitance matrix C and the resistance matrix R of the magnetic coupling wireless power transmission system into the practical characteristic equation | lambda of the magnetic coupling wireless power transmission system²[LC]+λ[RC]+I_n×n1 | ═ 0, give

f(λ)_actual＝λ²ⁿ+d_2n-1λ^2n-1+d_2n-2λ^2n-2…d₁λ+d₀； (1)

The inductance matrix comprises mutual inductance parameters to be determined, the capacitance matrix comprises capacitance parameters to be determined, the resistance matrix comprises resistance parameters to be determined, wherein,

L_mis the coil self-inductance of the mth circuit, R_mIs the resistance of the mth circuit, C_mIs a compensation capacitor of the mth circuit, M_mjIn order to obtain mutual inductance between the coil in the mth circuit and the coil in the jth circuit, m is 1,2, … n, j is 1,2, … n, n indicates the number of circuits of the magnetically coupled wireless power transmission system, I_n×nRepresenting an n × n-dimensional identity matrix, d_2n-1、d_2n-2、d₁And d₀To substitute L, C and R into | λ²[LC]+λ[RC]+I_n×nCoefficient obtained by | ═ 0;

s12: according to the magnetic coupling wireless power transmission system needsSatisfied frequency band number k, center frequency f_0,1,f_0,2…f_0,kAnd bandwidths b corresponding to the respective center frequencies₁,b₂…b_kDetermining a desired eigenvalue λ that meets the performance requirements_q＝-α_q+jω_qAnd

wherein, ω is_o,q＝2πf_0,q，B_q＝2πb_q,

r_qThe number of the q frequency band is the multiple number;

s13, obtaining the expected characteristic equation of the magnetic coupling wireless power transmission system according to the obtained expected characteristic value

a_2n-1、a_2n-2、a₁And a₀To be λ_q、

r_qQ is a coefficient obtained by substituting 1,2, … k for formula (2);

s14, determining a mutual inductance parameter, a capacitance parameter and a resistance parameter of the magnetic coupling wireless power transmission system according to the formula (1) and the formula (2);

the n, the q and the k are positive integers, the n is the number of circuits of the magnetic coupling wireless power transmission system, each circuit comprises a coil, and the k is less than or equal to n.

2. The method of claim 1, wherein R is a frequency and bandwidth based design of a magnetically coupled wireless power transfer system_mIs the sum of the coil internal resistance and the load resistance of the mth circuit.

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