CN108808889B - Resonance frequency calculation method of magnetic coupling wireless power transmission system - Google Patents

Abstract

The invention discloses a resonant frequency calculation method of a magnetic coupling wireless power transmission system, which realizes the quick solution of the resonant frequency by establishing a standard state space model of an arbitrary-order multi-transmission multi-relay multi-reception magnetic coupling wireless power transmission system. Furthermore, the analytical current of any tank can be calculated. The invention can make the system always in the maximum energy efficiency state according to the systematic working criterion by solving the resonance frequency.

Description

Resonance frequency calculation method of magnetic coupling wireless power transmission system

Technical Field

The invention relates to the technical field of wireless energy transmission, in particular to a resonance frequency calculation method of a magnetic coupling wireless power transmission system.

Background

The Magnetic coupling wireless power transmission system (MC-WPT) realizes the non-electrical connection transmission of electric energy from a power supply side to an electric equipment side, thoroughly gets rid of the constraint of a wire, has wide market prospect and scientific research value, and is widely applied to the fields of household appliances, biomedicine, electric vehicles and the like at present. As one of the inevitable development trends of the MC-WPT technology, a multi-transmitting, multi-relaying and multi-receiving wireless power transmission system has received high attention of researchers at home and abroad in recent years.

However, most of the current MC-WPT systems are based on the resonance coupling principle proposed by the american institute of technology and technology (MIT): the natural frequency and the power supply frequency of each oscillating circuit in the MC-WPT system are set to be consistent, so that a resonance state is realized, and the maximum energy efficiency is obtained. However, it is well known that this mode of energy transfer is ubiquitous in a physical phenomenon known as "frequency splitting": the system has a plurality of maximum energy efficiency points, corresponding frequencies deviate from the set inherent frequency of the circuit, and the system works in the set inherent frequency of the circuit and is low in energy efficiency. And the number and the position of the maximum energy efficiency points of the system in the phenomenon can be changed along with the change of the number of the resonators in the system. In addition, in a multi-coil structure system, even if a frequency splitting phenomenon does not exist, cross coupling between non-adjacent coils causes the maximum energy efficiency point of the system to deviate from the natural frequency of the arranged resonator, thereby causing low energy efficiency of the system. These phenomena greatly limit the energy efficiency of MC-WPT systems. All these phenomena indicate that, at least under certain parameter conditions (which exist mainly in practical systems), the existing energy transfer mode is not in a "resonance" state, i.e. the resonance point of the system is not the natural frequency point of the designed resonator.

In order to solve the problem of low system energy efficiency caused by these phenomena, many technical solutions have been proposed, such as frequency tracking control, increasing impedance matching network, adjusting system coupling strength, and so on. The methods of frequency tracking control, increasing impedance matching network, adjusting system coupling strength, etc. not only depend on specific system structures, that is, the specific methods of frequency tracking control, impedance matching network, etc. are different with different system structures, but also have respective inevitable disadvantages: the frequency tracking control is easy to converge to a local maximum point on one hand, and on the other hand, some additional circuits such as a detection circuit need to be added, so that the complexity of the system is increased; the addition of the impedance matching network increases the order of the system and also increases the complexity of the system; adjusting the coupling strength is generally achieved by mechanically adjusting the relative orientation or distance of the resonators, and thus this method is not suitable for systems where the resonators are fixed or where the resonators need to be moved constantly. In fact, these problems are present with the methods currently available, since these are essentially energy efficient compensation measures.

In order to solve the problems, the invention provides a resonance frequency calculation method of a magnetic coupling wireless power transmission system, which is used for solving the problems of low energy efficiency and energy transfer directivity caused by the frequency splitting phenomenon by disclosing the resonance mechanism of an MC-WPT system, establishing mathematical description between a resonance point and system parameters.

Disclosure of Invention

In order to solve the above problem, the present invention provides a resonant frequency calculation method for a magnetic coupling wireless power transmission system, wherein the resonant frequency calculation method comprises the following steps:

a resonance frequency calculation method of a magnetic coupling wireless power transmission system is characterized by comprising the following steps:

s 1: determining the order of the system and the circuit parameters of the system, wherein the circuit parameters comprise the following parameters: r_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_mM is 1-n, and n is the number of circuits; v. of_mAnd R_LmCannot coexist when v_mNot equal to 0 and R_LmCircuit m is a transmit circuit, whereas v is_m0 and R_LmNot equal to 0, the circuit m is a receiving circuit, and when both are 0, the circuit m is a relay circuit;

s 2: establishing a standard state space model of an arbitrary-order multi-transmitting multi-relay multi-receiving magnetic coupling wireless power transmission system:

to calculate a system matrix S; wherein:

state vector

Input vector v ═ v^T0_1×n]^T；I_n×nAn identity matrix representing order n; power supply voltage vector v ═ v₁v₂… v_n]^T(ii) a Current vector i ═ i₁i₂… i_n]^T(ii) a Capacitance voltage vector u ═ u₁u₂… u_n]^T；

Resistor matrix

R_m＝R_pm+R_LmRepresents the total resistance of the mth circuit;

capacitor matrix

Inductance matrix

S3, solving a characteristic value matrix Λ from the system matrix S;

λ_ifor the ith eigenvalue of the system matrix S,

is λ_iThe conjugate complex number of (a); i is 1 to n

s 4: according to [ omega ]_r,1ω_r,2… ω_r,n]Solving the resonance frequency of the system by | Im (eigenvalue (s)) | i.e. taking the absolute value of the imaginary part of 2n eigenvalues in the eigenvalue matrix Λ as the n resonance frequencies ω of the system_r,1，ω_r,2，…，ω_r,n。

The invention has the beneficial effects that: aiming at the problem that the frequency splitting phenomenon in the conventional magnetic coupling wireless power transmission system causes the uncertainty of the system resonance point, the invention provides a set of complete and systematic resonance mechanism modeling method and a resonance point calculation method. Compared with the prior art, the method has the following main advantages: the modeling analysis method and the resonance point calculation method can be suitable for a wireless electric energy transmission system with any order, multi-transmission, multi-relay, multi-receiving and no parameter constraint condition. The modeling analysis method not only can reveal the resonance mechanism of the MC-WPT system, but also can obtain the analytic expression of any loop current, and is beneficial to the optimization design of subsequent system parameters. A general analytical expression of the resonance point of the MC-WPT system is established, and a systematic working criterion is established for the system to work in the maximum energy efficiency state.

Drawings

FIG. 1 is a system circuit topology diagram of an embodiment of the present invention.

Detailed Description

In order to more clearly understand the technical features, objects, and effects of the present invention, embodiments of the present invention will now be described with reference to the accompanying drawings.

An equivalent circuit diagram of an arbitrary-order mimo wireless power transmission system is shown in fig. 1, where n circuits are sequentially denoted by subscripts 1,2, …, n. R_pmIs the internal resistance of the coil, L_mFor self-inductance of the coil, C_mFor corresponding compensation capacitance u_mTo compensate for the voltage across the capacitor, M_mjIs the mutual inductance between coil m and coil j, i_mIs the current of circuit m, R_LmIs the load of circuit m, v_mIs the power supply for circuit m. v. of_mAnd R_LmCannot coexist when v_mNot equal to 0 and R_LmCircuit m is a transmit circuit, whereas v is_m0 and R_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 law, the mathematical model of the equivalent circuit diagram can be expressed as:

wherein R is_m＝R_pm+R_LmRepresenting the total resistance of the mth tank.

Aiming at the mathematical model of the equivalent circuit diagram, the resonance frequency calculation method of the magnetic coupling wireless power transmission system is provided, and the purpose is to realize the calculation of the resonance frequency by constructing a state equation matched with the resonance frequency.

Specifically, the resonance frequency calculation method includes the steps of:

s 1: determining the order of the system and the circuit parameters of the system, wherein the circuit parameters comprise the following parameters: r_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 m electricityMutual inductance, i, between coil m in the line and coil j in the jth circuit_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;

s 2: the method comprises the following steps of establishing a standard state space model of any-order multi-transmitting multi-relay multi-receiving magnetic coupling wireless power transmission system:

wherein the content of the first and second substances,

state vector

Input vector v ═ v^T0_1×n]^T；

Wherein, I_n×nAn identity matrix representing order n; power supply voltage vector v ═ v₁v₂… v_n]^T(ii) a Current vector i ═ i₁i₂… i_n]^T(ii) a Capacitance voltage vector u ═ u₁u₂… u_n]^T；

Resistor matrix

Capacitor matrix

Inductance matrix

s 4: according to [ omega ]_r,1ω_r,2… ω_r,n]Obtaining | Im (eigenvalue(s) |The resonance frequency of the solution system, namely: the resonance frequency is the absolute value of the imaginary part of the eigenvalues of the system matrix S of the system.

Further, the method comprises a step s 3:

the eigenvalue matrix Λ and eigenvector matrix Φ are solved for the system matrix S, where,

wherein the content of the first and second substances,

and λ_iIs a complex conjugate;

wherein

And

is a complex conjugate;

the method further includes a step s5, where the analytic current of the mth oscillating loop is obtained as:

i_m＝Im(I_me^jωt)

wherein Im () represents the imaginary part of the complex number in the brackets, so that the analytic expression of each loop current of the multi-transmission multi-relay multi-reception MC-WPT system of any order can be obtained:

wherein ω represents the operating frequency; a is_q＝{ψ_q}^TA{ψ_q}，

In order to verify the feasibility of the solution, a corresponding mathematical derivation was performed with respect to the corresponding mathematical model of the equivalent circuit diagram shown in fig. 1.

Specifically, by defining a power supply voltage vector v, a current vector i, a capacitance voltage vector u, an inductance matrix L, a capacitance matrix C, and a resistance matrix R, the following are:

v＝[v₁v₂… v₃]^T,i＝[i₁i₂… i_n]^T,u＝[u₁u₂… u_n]^T

through equation transformation, the corresponding mathematical model of the equivalent circuit diagram shown in fig. 1 can be expressed as the following equation of state:

by introducing identity

And defining a state matrix

And the input matrix v' ═ v^T0_1×n]^TThe state equation may become:

wherein:

then will be

The normalization is as follows:

wherein the content of the first and second substances,

from matrix theory, it is known that there is a non-singular matrix such that the following equation holds. The nonsingular matrix is:

wherein, { ψ_qAnd

is a conjugated complex number, a_q＝{ψ_q}^TA{ψ_q}，

b_q＝{ψ_q}^TB{ψ_q}，

Where q is 1, 2.., n, where the subscript q denotes the qth column of the matrix Φ.

The equation is transformed by the above formula:

(-A^-1B)Φ＝SΦ＝ΦΛ

wherein the content of the first and second substances,

and

is the eigenvalue and eigenvector of the system matrix S, and thus, the matrices Φ, Λ,

and

can be obtained quickly.

According to equation (2), the state space model represented by equation (1) can be decoupled into 2n mutually independent equations:

wherein y ═ Φ^-1x。

Assuming the power supply frequency is omega, the power supply voltage v_mCurrent of circuit i_mAnd a capacitor voltage u_mCan be expressed as

Where | represents the amplitude of the variable in the brackets and Im () represents the imaginary part of the variable in the brackets, e.g.

Definition V ═ V₁V₂… V_n]^T，I＝[I₁I₂… I_n]^TAnd U ═ U₁U₂… U_n]^TWherein

The supply voltage vector v, the current vector i and the capacitor voltage vector u can be expressed as v-Im (Ve)^jωt)，i＝Im(Ie^jωt) And u ═ Im (Ue)^jωt). According to

And y ═ Φ^-1x, state vectorThe quantity y and the input vector v' may be expressed as y ═ Im (Ye)^jωt)，v'＝Im(V'e^jωt) Wherein Y is phi^-1[U^TωU^T]^TAnd V ═ V^T0_n×1]^T。

Changing y to Im (Ye)^jωt) And V '═ Im (V' e)^jωt) Substituted into the formula (3) to obtain

According to Y ═ phi^-1[U^TωU^T]^TAnd formula (4), can be given:

matrix phi_2n×2nWritable as a partitioned matrix

Wherein:

the block calculation is performed on the formula (5) to obtain a vector U of

From the relationship between the capacitor voltage and the capacitor current, I ═ ω CU can be obtained. The analytical expression for the capacitance vector i can thus be:

i＝Im(Ie^jωt)＝Im(ωCUe^jωt)

the current of all the oscillating loops in the system can be obtained, for example, the current of the mth oscillating loop can be expressed as

i_m＝Im(I_me^jωt)

For solving for the resonant frequency, the energy of the MC-PT system shown in FIG. 1 can be expressed as

The self-inductance in the MC-WPT system generally does not change along with the frequency, so the resonance of the MC-WPT system refers to the phenomenon that the amplitude of each loop current in the system is increased rapidly, and the resonance frequency refers to the system excitation frequency corresponding to the maximum value of the current amplitude. Theoretical derivation process of resonant frequency solution:

due to lambda_qIs the eigenvalue of the system matrix S, then is known according to the actual physical system characteristic, lambda_qIs a negative real number with a small absolute value. Thus λ_qAnd

may be respectively represented as lambda_q＝-α_q+jω_r,qAnd

α therein_qAnd ω_r,qIs positive and real and α_qAnd are typically small. From the previous formula can be represented as:

wherein:

when the operating frequency ω of the system is equal to ω_r,qWhen a plural number A_qThe mode of (a) is maximized by taking the maximum value,

due to α_qIs very small, therefore | A_q|_maxWill be provided withIs very large. According to the definition of resonance: the frequency corresponding to the maximum current amplitude is the resonant frequency of the system, so that:

if ω is_r,1,ω_r,2,...,ω_r,nSpaced far apart from each other, when the system operating frequency omega is equal to omega_r,qWhen the temperature of the water is higher than the set temperature,

will be much larger than others

And all of

In this case, it is preferable that the air conditioner,

the amplitude of each oscillation loop current of the system is maximum, namely the system is in a resonance state.

Conversely, if ω exists_r,qAnd ω_r,pClosely spaced, when the operating frequency of the system is ω equal to ω_r,qWhen the temperature of the water is higher than the set temperature,

and

will be large. In this case, it is preferable that the air conditioner,

magnitude of current | I_mThe maximum point of | will be at frequency ω_r,qAnd ω_r,pWithin the range. Due to omega_r,qAnd ω_r,pClosely spaced and therefore closer to the maximum point of the current amplitude, and therefore omega_r,qAnd ω_r,pCan be considered as the resonant frequency of the system.

According to the analysis result, n resonance frequencies (omega) exist in the n-coil structure MC-WPT system_r,1,ω_r,2,...,ω_r,n) They are system matrices SThe imaginary part of the characteristic value of (a). Unlike the natural frequency of each oscillating loop in the system of the conventional theory, the working frequency of the system is determined by the natural frequency, mutual inductance and resistance of all the oscillating loops in the system, as follows:

the invention provides a resonance mechanism modeling analysis method based on a vibration theory, and the method is suitable for any-order multi-input multi-output wireless power transmission systems. Based on the method, all the maximum energy efficiency frequency points of the system can be quickly and accurately obtained, so that a set of systematic working criterion is established for the system working in the maximum energy efficiency state. The analysis result firstly reveals the physical principle of resonance and frequency splitting, namely the natural frequency of the system is not the same concept with the natural frequency of each circuit in the system, and the system can resonate only when the power supply frequency is equal to the resonance frequency of the system. The fundamental reason for the frequency splitting phenomenon of the system is because the system has different natural frequencies of the system.

It should be noted that, for simplicity of description, the above-mentioned embodiments of the method are described as a series of acts or combinations, but those skilled in the art should understand that the present application is not limited by the order of acts described, as some steps may be performed in other orders or simultaneously according to the present application. Further, those skilled in the art should also appreciate that the embodiments described in the specification are preferred embodiments and that the acts and elements referred to are not necessarily required in this application.

In the above embodiments, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to related descriptions of other embodiments.

The above disclosure is only for the purpose of illustrating the preferred embodiments of the present invention, and it is therefore to be understood that the invention is not limited by the scope of the appended claims.

Claims (1)

1. A resonance frequency calculation method of a magnetic coupling wireless power transmission system is characterized by comprising the following steps:

s 1: determining the order of the system and the circuit parameters of the system, wherein the circuit parameters comprise the following parameters: r_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_mM is 1-n, and n is the number of circuits; v. of_mAnd R_LmCannot coexist when v_mNot equal to 0 and R_LmCircuit m is a transmit circuit, whereas v is_m0 and R_LmNot equal to 0, the circuit m is a receiving circuit, and when both are 0, the circuit m is a relay circuit;

s 2: establishing a standard state space model of an arbitrary-order multi-transmitting multi-relay multi-receiving magnetic coupling wireless power transmission system:

to calculate a system matrix S; wherein:

state vector

Input vector v ═ v^T0_1×n]^T；I_n×nAn identity matrix representing order n; power supply voltage vector v ═ v₁v₂… v_n]^T(ii) a Current vector i ═ i₁i₂… i_n]^T(ii) a Capacitance voltage vector u ═ u₁u₂… u_n]^T；

Resistor matrix

R_m＝R_pm+R_LmRepresents the total resistance of the mth circuit;

capacitor matrix

Inductance matrix

S3, solving a characteristic value matrix Λ from the system matrix S;

λ_ifor the ith eigenvalue of the system matrix S,

is λ_iThe conjugate complex number of (a); i is 1 to n

s 4: according to [ omega ]_r,1ω_r,2… ω_r,n]Solving the resonance frequency of the system by | Im (eigenvalue (s)) | i.e. taking the absolute value of the imaginary part of 2n eigenvalues in the eigenvalue matrix Λ as the n resonance frequencies ω of the system_r,1，ω_r,2，…，ω_r,n。

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