CN114928181A - Multi-relay MC-WPT system based on bilateral LCC compensation network and parameter design method - Google Patents
Multi-relay MC-WPT system based on bilateral LCC compensation network and parameter design method Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J50/00—Circuit arrangements or systems for wireless supply or distribution of electric power
- H02J50/50—Circuit arrangements or systems for wireless supply or distribution of electric power using additional energy repeaters between transmitting devices and receiving devices
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- G—PHYSICS
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- G06F30/32—Circuit design at the digital level
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J50/00—Circuit arrangements or systems for wireless supply or distribution of electric power
- H02J50/10—Circuit arrangements or systems for wireless supply or distribution of electric power using inductive coupling
- H02J50/12—Circuit arrangements or systems for wireless supply or distribution of electric power using inductive coupling of the resonant type
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J50/00—Circuit arrangements or systems for wireless supply or distribution of electric power
- H02J50/40—Circuit arrangements or systems for wireless supply or distribution of electric power using two or more transmitting or receiving devices
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J50/00—Circuit arrangements or systems for wireless supply or distribution of electric power
- H02J50/70—Circuit arrangements or systems for wireless supply or distribution of electric power involving the reduction of electric, magnetic or electromagnetic leakage fields
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Abstract
The invention provides a multi-relay MC-WPT system based on a bilateral LCC compensation network and a parameter design method, which are characterized in that: in consideration of the application scene limitation of the high-voltage transmission line on-line monitoring equipment, the LCC compensation network is only adopted at the transmitting end and the receiving end, and the relay coils are all compensated in series. Secondly, considering that resonance frequency deviation caused by frequency splitting and cross coupling mutual inductance may influence resonance conditions of the transmitting terminal compensation network and the receiving terminal compensation network, the invention provides three working modes according to resonance relations of the transmitting terminal compensation network, the relay coil compensation capacitor and the receiving terminal compensation network. The effect is as follows: the bilateral LCC compensation multi-relay MC-WPT system capable of quickly determining parameters of any coupling mechanism has system parameters and working frequency of constant voltage output characteristics or constant current output characteristics, and the system design of constant voltage output and constant current output of the multi-relay MC-WPT system is realized according to different application scenes by considering the influence of all cross coupling and frequency splitting on the system output characteristics.
Description
Technical Field
The invention relates to the technical field of MC-WPT (magnetic coupling wireless power transmission), in particular to a multi-relay MC-WPT system based on a bilateral LCC (link control channel) compensation network and a parameter design method of the multi-relay MC-WPT system based on the bilateral LCC compensation network.
Background
The wireless power transmission technology is a technology which comprehensively utilizes a power electronic technology and a modern control theory and realizes that electric energy is transmitted to a load from a power supply/battery in a non-electric contact mode through carriers such as a magnetic field, an electric field and the like, and has the advantages of safety, reliability, flexibility and the like. The technology is widely applied to the fields of biomedical implant equipment, smart phones, electric automobiles and the like.
In recent years, MC-WPT (magnetic coupling wireless power transfer) system analysis methods and system characteristic studies have been receiving more and more attention. In order to realize the constant voltage/constant current output characteristic of the multi-relay MC-WPT system, a special topological structure such as an LCC compensation network and a CLC compensation network is used, and the method is a commonly used method for realizing the constant voltage or constant current output characteristic. In such a two-sided LCC compensated multi-relay MC-WPT system, there are usually a plurality of resonance frequencies and constant current/constant voltage output frequencies, and the influence of the transmitting-side compensation network and the receiving-side compensation network on the system output characteristics is large. When analyzing the output characteristics of the dual-side LCC compensation multi-relay MC-WPT system, the resonance conditions of the transmitting end compensation network, the receiving end compensation network and the relay compensation network are inevitably considered at the same time. At present, for the constant voltage output control or the constant current output control of a double-side LCC compensation multi-relay MC-WPT system, the influence of the frequency splitting phenomenon in the multi-relay MC-WPT system on the resonance condition of a transmitting end compensation network and a receiving end compensation network is not considered, the resonance relation among the transmitting end compensation network, the relay compensation network and the receiving end compensation network is not considered at the same time, and the performance of the system is still to be improved.
Disclosure of Invention
The invention provides a multi-relay MC-WPT system based on a bilateral LCC compensation network and a parameter design method, and solves the technical problems that: how to avoid the influence of the frequency splitting phenomenon in the multi-relay MC-WPT system on the resonance condition of the transmitting end compensation network and the receiving end compensation network, and simultaneously considering the resonance relation among the transmitting end compensation network, the relay compensation network and the receiving end compensation network, under the condition of meeting the requirements of output voltage/current and output power, the constant voltage output or constant current output of the multi-relay MC-WPT system compensated by the LCC at two sides is realized, and higher energy transfer efficiency is kept.
In order to solve the technical problem, the invention provides a multi-relay MC-WPT system based on a bilateral LCC compensation network, which comprises a direct-current power supply, a high-frequency inverter, a transmitting end LCC compensation network and a transmitting coil L which are sequentially connected 1 Sequentially connected receiving coils L N Receiving end LCC compensation network, high-frequency rectifier and load R L Coupled in cascade at the transmitter coil L 1 And a receiving coil L N N-2 relay coils L in between 2 ,L 3 ,…,L N-1 Relay coil L 2 ,L 3 ,…,L N-1 Is correspondingly connected in series with a relay series compensation capacitor C 2 ,C 3 ,…,C N-1 Transmitting coil L 1 N-2 relay coils L 2 ,L 3 ,…,L N-1 Receiving coil L N Forming a coupling mechanism with N energy transmission coils, wherein N is more than or equal to 4; the transmitting end LCC compensation network comprises a transmitting end resonant inductor L p A first transmitting terminalSeries resonance capacitor C 1 And a transmitting terminal parallel resonance capacitor C p2 (ii) a The receiving end LCC compensation network comprises a receiving end resonant inductor L r The first receiving end is connected with a resonant capacitor C in series N And a receiving end parallel resonance capacitor C r2 。
Specifically, the transmitting end LCC compensation network further includes a second transmitting end series resonance capacitor C p1 The second transmitting terminal is connected in series with a resonant capacitor C p1 One end of the resonant inductor is connected with the transmitting end p The other end of the first capacitor is connected with the first emitting end series resonance capacitor C 1 A resonant capacitor C connected in parallel with the transmitting terminal p2 A common terminal of (a); the receiving end LCC compensation network further comprises a second receiving end series resonance capacitor C r1 The second receiving terminal is connected in series with a resonant capacitor C r1 One end of the resonant inductor L is connected with the receiving end r The other end is connected with the first receiving end series resonance capacitor C 6 Parallel resonance capacitor C with receiving end r2 To the common terminal.
Specifically, the value of the resonance parameter is determined according to the following resonance relationship:
wherein, ω is 1 、ω 2 And omega 3 Respectively a transmitting end resonant frequency, a relay resonant frequency and a receiving end resonant frequency.
Specifically, the direct current power supply is provided by an induction power taking device and a rectifier which are connected with each other, the induction power taking device takes power from a high-voltage power transmission line, and then the rectifier rectifies the power taken by the induction power taking device and outputs the direct current power supply.
The invention also provides a parameter design method, aiming at the multi-relay MC-WPT system based on the bilateral LCC compensation network, the parameter design method comprises the following steps:
s1, determining the DC power supply voltage U according to the practical application scene in System output power P out And a load resistance R L And determining the coupling machine according to design requirementsPhysical parameters of the structure;
s2, determining the self-inductance L of the transmitting coil based on the physical parameters of the coupling mechanism 1 And internal resistance R 1 Self-inductance L of N-2 relay coils 2 ,L 3 ,…,L N-1 And a corresponding internal resistance R 2 ,R 3 ,…,R N-1 Self-inductance L of the receiving coil N And internal resistance R N And a coil L i And a coil L j Mutual inductance between M ij I, j ≠ 1,2 ij ＝M ji ；
S3, constructing a (N-1) × (N-1) matrix
And (N-1) × (N-1) matrix
When ω is ω ═ ω 1 ＝ω 3 Time, receiving end LCC compensation network, high-frequency rectifier and load R L Are commonly equivalent to a resistor
Omega denotes the operating frequency of the high-frequency inverter, the high-frequency rectifier and the load R L Are commonly equivalent to a resistor
S4, determining the resonant frequency omega of the system circuit 0 By passing
Calculating to obtain C 2 ,C 3 ,…,C N-1 Further constructing a (N-1) × (N-1) matrix
C Ns Is ω ═ ω 1 ＝ω 3 Equivalent capacitance, C, of time-receiving-end LCC compensation network Ns ＝C 2 ＝C 3 ＝…＝C N-1 ；
S5, constructing matrix polynomial Q (λ) ═λ 2 L s +λR s +C s And 2(N-1) eigenvalues of Q (lambda) are obtained by calculating the spectrum of Q (lambda);
s6, according to the load resistance R L Determining all constant voltage output frequencies and constant current output frequencies in the 2(N-1) characteristic values according to the influence rule of the characteristic value distribution;
s7, determining the optimal constant voltage output frequency and the optimal constant current output frequency according to the magnitude, the attenuation rate and the sensitivity of the system output voltage/current under each constant voltage output frequency and each constant current output frequency;
s8, according to the design requirement of the system, firstly determining C p2 And C r2 An initial value of (1);
s9, determining values of other resonance parameters according to the optimal constant voltage/constant current output frequency and resonance relation, and adjusting C p2 And C r2 Up to the system output voltage U out Or system output current I out And system output power P out And the design requirement is met.
Further, in step S6, when the load resistance R is lower than the predetermined value L When the output end is short-circuited, the imaginary part of the characteristic value is determined as the constant voltage output frequency; when the load resistance R L When the output end is short-circuited, the imaginary part of the characteristic value is determined as the constant current output frequency.
The invention provides a multi-relay MC-WPT system based on a bilateral LCC compensation network and a parameter design method s 、R s 、C s And further determining all constant voltage output frequency and constant current output frequency by constructing a matrix polynomial to perform matrix operation to obtain a characteristic value, selecting the optimal constant voltage output frequency and the optimal constant current output frequency according to the difference of the magnitude, the attenuation rate and the sensitivity of system output voltage/current under each working frequency, and finally determining other resonance parameters of the system according to the selected frequency and the output of the system. The invention adopts a matrix operation mode to analyze the output characteristics of the system, does not need to process a large number of system parameters, and effectively simplifies the systemThe system analysis process is more remarkable particularly for high-order MC-WPT, not only constant voltage output characteristics and constant current output characteristics are realized in a bilateral LCC compensation multi-relay MC-WPT system, but also good performance is achieved (power meets design requirements, energy transfer efficiency is kept at a high level, and system attenuation rate and sensitivity are low), and in addition, voltage and current impact is hardly caused by load switching.
Drawings
Fig. 1 is a circuit topology diagram of a multi-relay MC-WPT system based on a double-sided LCC compensation network according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of a double-sided LCC compensation multi-relay MC-WPT system for high-voltage transmission line online monitoring equipment according to an embodiment of the present invention;
FIG. 3 is an equivalent circuit diagram of FIG. 1 provided by an embodiment of the present invention;
FIG. 4 is an equivalent circuit diagram of FIG. 3 provided by an embodiment of the present invention;
FIG. 5 is a coil profile of a coupling mechanism provided by an embodiment of the present invention;
FIG. 6 shows a characteristic λ of the mode A system according to an embodiment of the present invention k Dependent load resistance R L A change situation graph;
FIG. 7 shows the output voltage and output current of the mode A system with the operating frequency f and the load resistance R according to the embodiment of the invention L Varying the contour fill map;
FIG. 8 shows a characteristic λ of the mode B system according to an embodiment of the present invention k Dependent on load resistance R L A change situation graph;
FIG. 9 shows the output voltage and output current of the mode B system with the operating frequency f and the load resistance R according to the embodiment of the present invention L Varying the contour fill map;
FIG. 10 shows the output current I at a constant output frequency according to an embodiment of the present invention out Dependent load resistance R L A change situation graph;
FIG. 11 shows the output voltage U at the mode A constant voltage output frequency according to an embodiment of the present invention out Dependent on load resistance R L A change situation graph;
FIG. 12The output voltage U under the mode B constant voltage output frequency provided by the embodiment of the invention out Dependent load resistance R L A change situation graph;
fig. 13 is a parameter design flowchart of a dual-sided LCC compensated multi-relay MC-WPT system according to an embodiment of the present invention;
FIG. 14 is a graph of input voltage/current and output voltage waveforms for a system under test provided by an embodiment of the present invention;
FIG. 15 shows the output voltage U of the system in the experiment according to the embodiment of the present invention out Output power P out Sum efficiency η with load resistance R L A change situation graph;
fig. 16 is a dynamic waveform diagram of the output voltage of the system in the experiment according to the embodiment of the present invention.
Detailed Description
The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, which are given solely for the purpose of illustration and are not to be construed as limitations of the invention, including the drawings which are incorporated herein by reference and for illustration only and are not to be construed as limitations of the invention, since many variations thereof are possible without departing from the spirit and scope of the invention.
The embodiment of the invention firstly provides a multi-relay MC-WPT system (double-side LCC compensation multi-relay MC-WPT system) based on a double-side LCC compensation network, which comprises a direct-current power supply, a high-frequency inverter, a transmitting end LCC compensation network and a transmitting coil L which are sequentially connected 1 Sequentially connected receiving coils L N Receiving end LCC compensation network, high-frequency rectifier and load R L Coupled in cascade at the transmitting coil L 1 And a receiving coil L N N-2 relay coils L in between 2 ,L 3 ,…,L N-1 Relay coil L 2 ,L 3 ,…,L N-1 A relay series compensation capacitor C is correspondingly connected in series 2 ,C 3 ,…,C N-1 Transmitting coil L 1 N-2 relay coils L 2 ,L 3 ,…,L N-1 Receiving coil L N Forming a coupling mechanism with N energy transmission coils, wherein N is more than or equal to 4; the transmitting end LCC compensation network comprises a transmitting end resonant inductor L p A first emitting end connected in series with a resonant capacitor C 1 And a transmitting terminal parallel resonance capacitor C p2 (ii) a The receiving end LCC compensation network comprises a receiving end resonant inductor L r The first receiving end is connected with a resonant capacitor C in series N And a receiving end parallel resonance capacitor C r2 。
In this embodiment, a system analysis is performed by taking N as 6, that is, the total number of coils of the coupling mechanism is 6 (the number of relay coils is 4) as an example, and a circuit topology of the system is shown in fig. 1. i.e. i in (t) and i out (t) denotes the input and output currents, S, respectively 1 、S 2 、S 3 、S 4 Constituting an inverter. The inverter converts the direct-current power supply V into high-frequency alternating current and transmits the high-frequency alternating current to the coupling mechanism. The coupling mechanism consists of a transmitting coil, a relay coil and a receiving coil. L is a radical of an alcohol 1 Indicating the self-inductance of the transmitting coil, L 6 Indicating the self-inductance of the receive coil. The number of relay coils is 4, L 2 、L 3 、L 4 、L 5 Indicating the self-inductance of the relay coil. M ij Indicating the coil L i And a coil L j Mutual inductance between (i, j ≠ j, M) 1,2 ij ＝M ji ). Each relay coil is connected in series with a compensation capacitor. C 2 、C 3 、C 4 、C 5 The compensation capacitances of the respective relay coils are respectively indicated. R is i Indicating the coil L i An Equivalent Series Resistance (ESR) of (i ═ 1, 2.., 6). i.e. i 1 (t)、i 2 (t)、i 3 (t)、i 4 (t)、i 5 (t)、i 6 (t) represents the current of each coil. The high-frequency alternating current at the receiving end is converted into a direct current power supply suitable for supplying power to the on-line monitoring equipment after passing through the rectifying and filtering circuit. D 1 、D 2 、D 3 、D 4 Form a high-frequency rectifier, C L Representing the filter capacitance. R Leq The equivalent resistance representing the rectifier and the load resistance can be calculated by equation (1).
Transmitting end resonance inductor L p A first emitting end connected in series with a resonant capacitor C 1 And a transmitting terminal parallel resonance capacitor C p2 Forming a transmitting end LCC compensation network and a receiving end resonant inductor L r The first receiving end is connected with a resonant capacitor C in series 6 And receiving end parallel resonance capacitor C r2 And forming a receiving end LCC compensation network. Wherein L is p Can also use L p And C p1 Instead, i.e. the transmitting end LCC compensation network further comprises a second transmitting end series resonance capacitor C p1 The second transmitting terminal is connected in series with a resonant capacitor C p1 One end is connected with a transmitting end resonance inductor L p The other end is connected with a first emitting end series resonance capacitor C 1 A resonant capacitor C connected in parallel with the transmitting terminal p2 To the common terminal. L is a radical of an alcohol r Can also use L r And C r1 Instead, i.e. the receiving-end LCC compensation network further comprises a second receiving-end series resonance capacitor C r1 The second receiving end is connected in series with a resonant capacitor C r1 One end is connected with a receiving end resonance inductor L r The other end is connected with a first receiving end series resonance capacitor C 6 Parallel resonance capacitor C with receiving end r2 To the common terminal. C p1 And C p2 The voltage (or current) impact caused by the switching of the load resistance can be effectively reduced by the addition of the resistor, and a certain protection effect is achieved.
As a specific application, a schematic structural diagram of a double-side LCC compensation multi-relay MC-WPT system for power supply of the high-voltage transmission line online monitoring device is shown in fig. 2. The whole system consists of an induction electricity taking device (electricity taking CT, wherein CT is the abbreviation of current transformer and represents a current transformer), a high-frequency inverter, a transmitting terminal compensation network, a coupling mechanism, a receiving terminal compensation network, a high-frequency rectifier and a load. The high-voltage transmission line (HVTL) is installed in the power CT to collect energy from the surrounding alternating magnetic field, and the energy is transmitted to the coupling mechanism and the compensation network after passing through the rectifier and the high-frequency inverter, and finally the electric energy is converted into direct current suitable for supplying power to a load (such as an online monitoring device) through the high-frequency rectifier at the receiving end. And a transmitting coil, a relay coil and a receiving coil of the coupling mechanism are all installed and fixed in the insulator.
The equivalent circuit diagram of the double-side LCC compensation multi-relay MC-WPT system is shown in figure 3. The transmitting end compensation network comprises L p 、C p1 、C p2 And C 1 . The receiver compensation network comprises L r 、C r1 、C r2 And C 6 。i in (t) and i out (t) represents the input current and the output current, respectively. The high frequency inverter and the dc power source V in fig. 1 are equivalent to an ac voltage source u (t). Because the multi-relay MC-WPT system has good low-pass filtering performance, higher harmonics can be effectively eliminated. Therefore, u (t) can be represented by equation (2), and ω represents the operating frequency of the high frequency inverter.
This embodiment defines the matrix L, the matrix R, and the matrix C as follows:
according to kirchhoff's voltage law, the eigen equation of a two-sided LCC compensated multi-relay MC-WPT system can be expressed as:
where N is 6, where L, R, C are all 8 × 8 matrices, i (t) ═ i in (t)i 1 (t)…i 6 (t)i out (t)] T ，H＝[1 0…0] T 。
For multi-relay MC-WPT, the number of system parameters will increase rapidly as the number of relay coils increases. However, as can be seen from equation (6), the system output is closely related to the three matrices, and all system parameters are included in the three parameter matrices. After modeling is carried out on the double-side LCC compensation multi-relay MC-WPT system, a large number of system parameters do not need to be processed, and the output characteristics of the system are analyzed through matrix operation. The system analysis process is effectively simplified, and is particularly remarkable for high-order MC-WPT. The output characteristic of the double-sided LCC compensation multi-relay MC-WPT system proposed in this embodiment can also be obtained by solving L, R, C secondary eigenvalues.
Because the compensation networks of the transmitting end and the receiving end both adopt the LCC compensation network, the characteristics and resonance conditions of the LCC compensation network can be utilized, and the equivalent circuit model of the system is further simplified. Firstly, the eigen equation of the double-side LCC compensation multi-relay MC-WPT system is reduced. This embodiment defines ω separately 1 、ω 2 And ω 3 Respectively a transmitting end resonant frequency, a relay resonant frequency and a receiving end resonant frequency. The correspondence between the compensation network parameters and the three resonant frequencies is as follows:
in particular, when the resonance frequency ω of the relay 2 Equal to the receiving end resonant frequency omega 3 Meanwhile, the receiving end compensation network parameters can be calculated by equation (8).
According to the corresponding relationship between the compensation network parameter and the resonant frequency in the equation (7), when ω is ω ═ ω 1 ＝ω 3 The system equivalent circuit can be further simplified to a simplified equivalent circuit as shown in fig. 4.
L s 、R s 、C s Three system matrices representing simplified equivalent circuits. By rotatingBy converting the formula (3), the formula (4) and the formula (5), L can be obtained s 、R s 、C s The expression of (a) is as follows:
R Leqs representing the receiver compensation network and the equivalent load resistance R Leq The equivalent load resistance of (2) is a load resistance in a simplified equivalent circuit, and the expression is as follows:
C Ns ＝C 2 ＝C 3 ＝…＝C N-1 ，C Ns and compensating the equivalent capacitance of the network for the LCC at the receiving end.
i p (t) represents an equivalent current source, and the expression is as follows:
by means of a matrix L s Matrix R s Sum matrix C s The eigen equation expression of the simplified equivalent circuit of the double-side LCC compensation multi-relay MC-WPT system is as follows:
wherein L is s 、R s And C s Are all 5 × 5 matrices, H s ＝-[M 12 M 13 …M 16 ] T ，i s (t)＝[i 2 (t)…i 6 (t)] T 。
Through simplification, the 8-order MC-WPT system is reduced to a 5-order MC-WPT system. R s And C s Are all converted into a diagonal matrix. In general, L s Is a diagonal dominant matrix, therefore L s Is a non-singular matrix. L is s 、R s And C s Are all true symmetric positive definite matrices. All eigenvalues are real or in conjugate complex pairs (λ, λ) * ) Only half of the eigenvalues need to be analyzed.
Q (lambda) is a constructed matrix polynomial as shown in formula (15). Λ (Q) is a spectrum of Q (λ), representing a set of characteristic values of Q (λ), as shown in equation (16).
Q(λ)＝λ 2 L s +λR s +C s (15)
Wherein, diag (λ) 1 ,λ 2 ,…,λ 2(N-1) ) Is expressed as λ 1 ,λ 2 ,…,λ 2(N-1) Is a diagonal matrix of diagonal elements.
X, Y denotes the eigenvector of Q (λ), x k 、y k Respectively represent corresponding lambda k A right and left eigenvector of (k ═ 1,2,. 2 (N-1)).
According to equations (16) and (17), the steady-state induced current expression of the system simplified equivalent circuit is as follows:
the present example was studied using a 6-coil MC-WPT system as an example, but it should be noted that the proposed method can also be extended to other N-coil MC-WPT systems (less or more than 6 coils).
The equivalent circuit model shown in fig. 3 and the simplified equivalent circuit model shown in fig. 4 can obtain the output characteristics of the double-sided LCC compensated multi-relay MC-WPT system using a secondary eigenvalue-based analysis method. The analysis method based on the secondary characteristic value mainly comprises the following two steps: firstly, analyzing the influence rule of the load resistance on the characteristic value, and then solving according to the relation between the system output characteristic and the characteristic value to obtain the key frequency (constant current output frequency and constant voltage output frequency).
It should be noted that, for the double-sided LCC compensated multi-relay MC-WPT system, in addition to the relay coil and its compensation capacitor in the coupling mechanism, the influence of the transmitting end compensation network and the receiving end compensation network on the output characteristics of the system needs to be considered. Therefore, according to the resonance relationship among the transmitting end compensation network, the relay coil compensation capacitor and the receiving end compensation network, three working modes are provided, the working principle of each working mode is analyzed, the output characteristics of the three working modes are researched, the performances of the three working modes are compared, and finally, a parameter design method of the double-side LCC compensation multi-relay MC-WPT system is provided based on research results, so that the constant voltage or constant current output of the double-side LCC compensation multi-relay MC-WPT system is realized under the condition that the cross coupling and the coupling mechanism equivalent series resistance are considered.
A6-coil MC-WPT system is used for demonstrating a method for obtaining constant voltage or constant current output characteristics in three working modes. The coil distribution structure of the 6-coil MC-WPT system is shown in fig. 5, the normals of all the coils are in the same direction, and the transmission distances d between adjacent coils are the same. The simulation system parameters are shown in table 1. The coupling mechanism parameters were obtained from COMSOL simulation, and the specific mutual inductance parameters are shown in table 2.
TABLE 1 simulation System parameters
TABLE 2 mutual inductance parameters of the coupling mechanism
In a multi-relay MC-WPT system, there are usually a plurality of resonance frequencies and constant current/constant voltage output frequencies, which can be obtained by solving the relationship between the characteristic values and the system output characteristics. However, for the dual-side LCC compensation multi-relay MC-WPT system proposed in this embodiment, the influence of the transmitting-end compensation network and the receiving-end compensation network on the system output characteristics is large. When analyzing the output characteristics of the dual-side LCC compensation multi-relay MC-WPT system, the resonance conditions of the transmitting end compensation network, the relay compensation network and the receiving end compensation network are inevitably considered at the same time. Therefore, the present embodiment proposes three operation modes according to the resonance conditions of the transmitting end compensation network, the relay compensation network, the receiving end compensation network and the relay coil compensation capacitor. The transmitting end of each working mode compensates the resonance frequency omega of the network 1 Receiving end compensation network resonant frequency omega 2 And the resonance frequency omega of the compensation capacitor of the relay coil 3 The relationship between them is shown in table 3. Omega 0 Is a fixed value representing the system circuit frequency. In MC-WPT system design, an approximate range of operating frequencies, therefore ω 0 Will be determined first. For multi-relay MC-WPT systems, the operating frequency ω 0 Typically between 100kHz and 500kHz, but there is no fixed requirement for the resonant frequency and is not strictly limited to this range. The variation parameter in table 3 refers to a resonance frequency at which the system output characteristic or the system gain can be changed by adjusting the value thereof. It should be noted that a variation parameter refers to a change in the design process of a system parameter, and all parameters are constant while the system is operating. The double-side LCC multi-relay MC-WPT system provided by the embodiment operates in an open loop mode, and the constant voltage or constant current output characteristic can be realized without an additional control method.
TABLE 3 comparison of resonant frequency relationships for three operating modes
With respect to mode A: the critical frequencies (constant current output frequency and constant voltage output frequency) of a multi-relay MC-WPT system typically do not contain ω 0 . When the system operates at these critical frequencies, it can cause the resonance conditions of the transmit and receive compensation networks to be violated. In most application scenarios, the multi-relay MC-WPT system has multiple critical frequencies (constant current output frequency and constant voltage output frequency), so that it is not necessary to purposely adjust omega by compensating network parameters or other control methods 0 The frequency is designed to be constant current or constant voltage output. To avoid this, the following two modes of operation are proposed.
With respect to mode B: as can be seen from the resonant frequency relationship of mode B, when the system operates in mode B, the resonant frequency of the transmission-side compensation network is always equal to the operating frequency. The resonance condition of the transmitting end compensation network and the receiving end compensation network cannot be damaged due to the change of the working frequency, and the system can work at each key frequency (constant current output frequency and constant voltage output frequency) to obtain corresponding system output characteristics.
And a mode C: unlike mode B, in mode C, the system achieves constant current or constant voltage output characteristics by changing the resonant frequency ω of the compensation capacitor of the relay coil 2 To change the critical frequency of the system (constant current output frequency and constant voltage output frequency). The working frequency is fixed and is the same as the resonance frequency of the transmitting end compensation network and the receiving end compensation network. By varying omega 2 The system can also be operated at various critical frequencies to obtain corresponding system output characteristics.
As can be seen from table 3, the fixed parameters of pattern B are the same as the varying parameters of pattern C, the fixed parameters of pattern C are the same as the varying parameters of pattern B, and the varying parameters of the two patterns are opposite to the fixed parameters. Therefore, when analyzing and comparing the output characteristics of the system in the three modes, only one of the mode B and the mode C needs to be selected for research.
Research system under different working modesThe output characteristic is mainly divided into two parts, firstly, the characteristic value lambda is studied k Dependent load resistance R L And obtaining the constant voltage output frequency and the constant current output frequency according to the relation between the characteristic value and the system output characteristic according to the change rule.
First, the working mode A is studied, according to equation (16), the characteristic value λ k As a function of load resistance R L The variation is shown in fig. 6 (k ═ 1, 2., 8). The horizontal axis (Re) represents the real part of the eigenvalue, and the vertical axis (Im) represents the imaginary part of the eigenvalue. With load resistance R L Increasing from 0 Ω to 1000 Ω, the real and imaginary parts of the 8 eigenvalues vary along the direction shown by the arrows in the figure.
As can be seen from fig. 6, the number of coils of the double-sided LCC compensation multi-relay MC-WPT system proposed in this embodiment is 6, but the system is an 8-step system and coexists in 8 eigenvalues. The compensation networks of the transmitting end and the receiving end both comprise a loop, and each loop needs to construct an equation according to kirchhoff voltage law, so that L, R, C matrixes are 8 x 8 matrixes and coexist in 8 eigenvalues. It can also be seen from the increase in the number of eigenvalues that the LCC compensation networks at both the transmitting and receiving ends are detuned. These two additional tanks exacerbate the frequency splitting phenomenon, resulting in the appearance of two additional system resonance frequencies.
With load resistance R L Gradually increasing of, λ 3 The real part of (a) will gradually decrease to be much smaller than the other eigenvalues. According to equation (18), the real parts of the eigenvalues are all negative numbers when λ 3 When the real part of the system is far smaller than other eigenvalues, the output characteristic of the system is only influenced by other 7 eigenvalues. In particular, λ 3 Will approach 0, when the number of system resonance frequencies is reduced from 8 to 7. When the load resistance approaches 0 Ω or infinity, the imaginary parts of all the characteristic values gradually approach a fixed frequency.
When the load resistance approaches 0 (equivalent to short circuit at output end), the imaginary part of the 8 characteristic values is weak damping frequency, i.e. constant voltage output frequency ω CV The expression is shown in formula (19). When the load resistance approaches infinity (equivalent to an open circuit at the output terminal), except for λ 3 The imaginary parts of the other 7 characteristic values are strong damping frequency and constant current output frequency omega CC The expression is shown in formula (20).
Output voltage U according to equation (18), mode A out And an output current I out With operating frequency f and equivalent load resistance R Leq The varying contour fill pattern is shown in figure 7. The abscissa represents the load resistance R L The ordinate represents the operating frequency f, and the black dotted line represents Im (λ) k )/2π(k＝1,2,…,8)。
As can be seen from fig. 7, when the system operates at a strong damping frequency (constant current output frequency), the output current I is out Can be kept constant over the entire load resistance range. The output voltage can be kept substantially constant over the entire load resistance range when the system is operating at a weakly damped frequency. From the number of critical frequencies, mode a seems to be better, with 8 constant voltage output frequencies and 7 constant current output frequencies. However, from the frequency sensitivity point of view, far from the system circuit frequency ω 0 Is sensitive with respect to the operating frequency, in particular lambda 1 、λ 2 、λ 7 And λ 8 The corresponding critical frequency is not suitable as the system operating frequency.
When the system is operating in mode B, the eigenvalues λ are according to equation (16) k Variation of R with load resistance L The variation is shown in fig. 8 (k ═ 1, 2., 8). The horizontal axis (Re) represents the real part of the eigenvalue, and the vertical axis (Im) represents the imaginary part of the eigenvalue. With load resistance R L Increasing from 0 Ω to 1000 Ω, the real and imaginary parts of the 5 eigenvalues vary along the direction shown by the arrows in fig. 8.
As can be seen from fig. 8, the dual-sided LCC patch proposed in this embodimentThe number of coils of the multi-relay MC-WPT system is 6, but the system is a 5-order system and coexists in 5 characteristic values. The reasons for this are: since the working frequency in mode B is always equal to the resonance frequency of the compensation network at the transmitting end and the resonance frequency of the compensation network at the receiving end, the system matrix L s 、R s 、C s It is reduced to a 5 × 5 matrix, and thus 5 eigenvalues coexist. It can also be seen from the reduction of the number of characteristic values that the transmitting side compensation network and the receiving side compensation network always maintain the resonance state. The frequency splitting is now performed by the remaining 5 coils (L) 2 、L 3 、L 4 、L 5 、L 6 ) Resulting in, and therefore reducing, a system resonant frequency.
It should be noted that although the number of the eigenvalues and the system resonant frequency may vary according to the operation mode, this does not mean that a certain eigenvalue and system resonant frequency corresponding to the transmission-side compensation network or the receiving-side compensation network "appears" or "disappears". Eigenvalues and system resonant frequencies of a multi-relay MC-WPT system are inherent properties of the system as a whole, which are related only to the system architecture and system parameters.
Unlike mode A, with load resistance R L Is gradually reduced by λ 5 Will gradually decrease to much less than the other eigenvalues. According to equation (18), the real parts of the eigenvalues are all negative numbers when λ 5 Is far smaller than the other eigenvalues, the output characteristics of the system are only affected by the other 4 eigenvalues. In particular, λ 5 Will approach 0, where the number of system resonance frequencies is reduced from 5 to 4. When the load resistance approaches 0 Ω or infinity, the imaginary parts of all the characteristic values gradually approach a certain fixed frequency.
The reason why the change tendency of the characteristic value of the pattern B is opposite to that of the pattern a is: the receiving end compensation network adopts an LCC compensation network, a receiving end LCC compensation network and an equivalent load resistor R Leq Equivalent load R of Leqs As shown in the formula (12), it can be seen that the load resistance R of the equivalent circuit is simplified Leqs And the actual load resistance R L Inversely proportional, therefore, the direction of change of the characteristic value of the mode B is equal toMode a is reversed. The same is true. The same is true of the direction of change of the characteristic value of the mode C.
Since the load resistance has different influence rules on the characteristic value, the calculation method of the critical frequency also needs to be changed. When the load resistance approaches infinity (equivalent to an open circuit at the output end), the imaginary part of the 5 characteristic values is a weak damping frequency, i.e. the constant voltage output frequency ω CV The expression is shown in formula (21). When the load resistance approaches 0 (equivalent to short circuit at the output terminal), except for λ 5 The imaginary parts of the other 4 characteristic values are strong damping frequency and constant current output frequency omega CC The expression is shown in formula (22).
According to equation (18), output voltage U of mode B out And an output current I out With operating frequency f and equivalent load resistance R Leq The varying contour fill pattern is shown in figure 9. The abscissa represents the load resistance R L The ordinate represents the operating frequency f, and the black dotted line represents Im (λ) k )/2π(k＝1,2,…,8)。
As can be seen from fig. 9, when the system is operated at a strong damping frequency (constant current output frequency), the output current I is out Can be kept constant over the entire load resistance range. Output voltage U when system is working at weak damping frequency out Can be kept substantially constant over the entire load resistance range. The number of critical frequencies of mode B is less than that of mode a in terms of the number of critical frequencies, and only has 4 constant voltage output frequencies and 5 constant current output frequencies. However, from the frequency sensitivity point of view, only 1 is far away from the system circuit frequency ω 0 Is relatively sensitive with respect to the operating frequency, i.e. λ 4 The corresponding critical frequency.
The overall key frequencies (constant current output frequency and constant voltage output frequency) of the system in both modes of operation are summarized in table 4. In order to improve the performance of the system, the most suitable operating frequency is selected from all the key frequencies of the mode a and the mode B, and the constant voltage output characteristic and the constant current output characteristic of the mode a and the mode B are analyzed and compared in detail in aspects of attenuation rate, gain and the like of system output voltage/current.
TABLE 4 Key frequencies for mode A and mode B
Considering that there are multiple constant current output frequencies and multiple constant voltage output frequencies in both operating modes, in order to simplify the analysis and comparison process, in this embodiment, first, 3 key frequencies with better performance in each mode are selected from the mode a and the mode B, and then, the advantages and disadvantages of the mode a and the mode B are analyzed and compared by comparing the 6 operating frequencies. Mode A selection of λ 4 、λ 5 And λ 6 Corresponding key frequencies (constant voltage output frequency and constant current output frequency), and the mode B selects lambda 2 、λ 3 And λ 5 Corresponding constant voltage output frequency and lambda 1 、λ 2 And λ 3 And (4) corresponding constant current output frequency.
In terms of constant current output characteristics, mode a and mode B output current I at a constant current output frequency out Dependent on load resistance R L The variation is shown in fig. 10. As can be seen from the figure, when the load resistance is small (less than 10 Ω), the output current in mode B gradually decreases, which means that mode B cannot maintain its constant current output characteristic at light load. Although the mode a can maintain its constant current output characteristic when the load resistance is small, the rate of attenuation of its output current with the increase of the load resistance is much greater than that of the mode B. In summary, the constant current output characteristic of the mode B is superior to that of the mode a over the entire load variation range.
Mode A outputs the voltage U in terms of constant voltage output characteristics out As a function of load resistance R L The situation is as shown in FIG. 11(a), mode B inputOutput voltage U out Dependent load resistance R L The variation is shown in FIG. 12 (a). C is to be p2 And C r2 Changing to 2.5nF, other compensation network parameters can be calculated from equation (7), and the output voltage U for mode A and mode B is then obtained out Variation of R with load resistance L The situation is shown in fig. 11(b) and 12 (b). As a whole, there is no great difference between the output voltage decay rates of the two operation modes, wherein the output voltage decay rate of mode B is slightly higher than that of mode A. Note, however, that the output voltage of the mode a cannot maintain the constant voltage output characteristic when the load resistance is small (less than 10 Ω).
As can be seen by comparing fig. 11 and 12, the output voltage gain of mode a remains approximately 1 constant at all times. Even by adjusting the compensating network parameter C p2 And C r2 The output voltage gain is not changed either. The main reason is that the LCCs at the transmitting end and the receiving end compensate for the network detuning, resulting in the loss of the function of adjusting the output gain. This can severely limit the range of applications (e.g., in-line monitoring devices), meaning that an additional chopper circuit is required to regulate the output voltage. For mode B, the LCC compensation networks at the transmitting and receiving ends are always not detuned, and thus their effect of adjusting the output gain can be maintained.
Based on the working principle analysis and the output characteristic research of the three working modes of the double-side LCC compensation multi-relay MC-WPT system, a parameter design flow shown in FIG. 13 is given below. In the flow chart 13, the input voltage U in Output power P out Load resistance R L The range and the coupling mechanism geometry depend mainly on the actual application scenario.
For mode B, the more specific parameter design flow of the present invention is as follows:
s1, determining the DC power supply voltage U according to the practical application scene in System output power P out And a load resistance R L Determining physical parameters (mainly comprising the number of turns of the coil, the number of layers of the coil, the number of the coils N, the wire diameter, the radius of the coil and the transmission distance d) of the coupling mechanism according to design requirements;
s2 determining emission based on physical parameters of coupling mechanismSelf-inductance L of coil 1 And internal resistance R 1 Self-inductance L of N-2 relay coils 2 ,L 3 ,…,L N-1 And a corresponding internal resistance R 2 ,R 3 ,…,R N-1 Self-inductance of the receiving coil L N And internal resistance R N And a coil L i And a coil L j Mutual inductance M between ij I, j ≠ j, M, N, and i ≠ j ij ＝M ji Adjusting the geometric parameters of the coupling mechanism until the parameters such as the mutual inductance M meet the design requirements;
s3, constructing a (N-1) × (N-1) matrix
And (N-1) × (N-1) matrix
When ω is ω ═ ω 1 ＝ω 3 Time, receiving end LCC compensation network, high-frequency rectifier and load R L Are commonly equivalent to a resistor
Omega denotes the operating frequency of the high-frequency inverter, the high-frequency rectifier and the load R L Are commonly equivalent to a resistance
S4, determining the resonant frequency omega of the system circuit 0 By passing
Calculating to obtain C 2 ,C 3 ,…,C N-1 Further constructing a (N-1) × (N-1) matrix
C Ns Is ω ═ ω 1 ＝ω 3 Equivalent capacitance, C, of time-receiving-end LCC compensation network Ns =c 2 =c 3 =...=c N-i ;
S5, constructing a matrix polynomial Q (lambda) ═ lambda 2 L s +λR s +C s And 2(N-1) eigenvalues of Q (lambda) are obtained by calculating the spectrum of Q (lambda);
s6, according to the load resistance R L Determining all constant voltage output frequencies and constant current output frequencies in the 2(N-1) characteristic values according to the influence rule of the characteristic value distribution;
s7, determining the optimal constant voltage output frequency and the optimal constant current output frequency according to the magnitude, the attenuation rate and the sensitivity of the system output voltage/current under each constant voltage output frequency and each constant current output frequency;
s8, according to the design requirement of the system, firstly determining C p2 And C r2 An initial value of (1);
s9, determining the values of other resonance parameters according to the optimal constant voltage/constant current output frequency and resonance relation, and adjusting C p2 And C r2 Up to the system output voltage U out Or system output current I out And system output power P out And the design requirement is met.
In step S6, as before, when the load resistance R L When the output end is short-circuited, the imaginary part of the characteristic value is determined as the constant voltage output frequency; when the load resistance R L When the output end is short-circuited, the imaginary part of the characteristic value is determined as the constant current output frequency.
In step S7, the magnitude, attenuation rate and sensitivity of the system output voltage/current need to be considered in combination with actual requirements.
In step S8, the system design requirement specifically refers to the system output power P out Output voltage U out Output current I out And the like.
In step S9, the specific manner of adjusting the parameters is as follows: when the output voltage U is out Or output current I out When the design requirement of the system is less than the requirement, C needs to be increased appropriately p2 And C r2 A value of (d); when outputting the voltage U out Or output current I out When the design requirement of the system is larger, C needs to be reduced properly p2 And C r2 The value of (c).
In order to verify the method, a 6-coil MC-WPT system experimental device is built in the embodiment and consists of a programmable direct-current power supply (ITECH IT6535D), an inverter, a direct-current electronic load (ITECH IT8512A +), an upper computer and a digital oscilloscope (Tektronix TPS 2024B). The 6 coils are formed by winding litz wires. The inverter uses SiC MOSFETs (IMZ120R045M1) as switching devices and a DSP (TMS320F28335) as controller to control the switching state of each switching tube and associated protection circuitry based on TI programming.
The coupling mechanism geometry parameters are the same as the simulation parameters shown in table 1. The measured parameters of the coupling mechanism are shown in table 5, the measured parameters of the compensation network are shown in table 6, and the measured parameters of the experimental device are measured by an electric bridge (HIOKI IM 3536).
TABLE 5 coupling mechanism parameters
TABLE 6 compensating network parameters for the experimental setup
The performance of the two-sided LCC compensated multi-relay MC-WPT system in mode B was evaluated by this 25W experimental setup.
Regarding the constant voltage output characteristics, the operating frequency of the experimental device was 367.6kHz, which is one of 5 constant voltage output frequencies. The voltage of the direct current power supply V is 50V. The voltage and current waveforms of the system are shown in fig. 14. u. of in And i in Respectively representing input voltage and input current waveforms u out Representing the output voltage waveform. Input voltage effective value I in Is 1.22A. Effective value of output voltage U out 50.86V. It can be seen from the figure that there is a phase difference between the input voltage and the input current. At this time, the system outputs a voltage U out Output power P out Sum efficiency η with load resistance R L The variation is shown in fig. 15 (a). When the load resistance R L When the voltage is reduced from 200 omega to 100 omega, the output voltage is reduced from 50.86V to 49.52V, and the attenuation rate is 2.6%. In thatWhen the load resistance is equal to 100 omega, the overall efficiency from the direct current end of the system to the direct current end can reach 79.5 percent.
Fig. 16 shows the dynamic process of the experimental device during the load resistance switching. From the figure, it can be seen that both the constant voltage output characteristic and the constant current output characteristic have been achieved in the double-sided LCC compensated multi-relay MC-WPT system and have good performance. In addition, load switching causes little voltage and current surge. The transmission power range of the experimental device is 12W to 25W, and the power requirements of most of on-line monitoring equipment can be met.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (6)
1. A multi-relay MC-WPT system based on a bilateral LCC compensation network is characterized in that: the system comprises a direct current power supply, a high-frequency inverter, a transmitting terminal LCC compensation network and a transmitting coil L which are sequentially connected 1 Sequentially connected receiving coils L N Receiving end LCC compensation network, high-frequency rectifier and load R L Coupled in cascade at the transmitter coil L 1 And a receiving coil L N N-2 relay coils L in between 2 ,L 3 ,…,L N-1 Relay coil L 2 ,L 3 ,…,L N-1 Is correspondingly connected in series with a relay series compensation capacitor C 2 ,C 3 ,…,C N-1 (ii) a Transmitting coil L 1 N-2 relay coils L 2 ,L 3 ,…,L N-1 Receiving coil L N Forming a coupling mechanism with N energy transfer coils, wherein N is more than or equal to 4; the transmitting end LCC compensation network comprises a transmitting end resonant inductor L p A first emitting end connected in series with a resonant capacitor C 1 And a transmitting terminal parallel resonance capacitor C p2 (ii) a The receiving end LCC compensation network comprises a receiving end resonant inductor L r The first receiving end is connected with a resonant capacitor C in series N And a receiving end parallel resonance capacitor C r2 。
2. The multi-relay MC-WPT system based on double-sided LCC compensation network of claim 1, wherein: the transmitting terminal LCC compensation network further comprises a second transmitting terminal series resonance capacitor C p1 Second transmitting terminal connected in series to resonant capacitor C p1 One end of the resonant inductor is connected with the transmitting end p The other end of the first capacitor is connected with the first emitting end series resonance capacitor C 1 A resonant capacitor C connected in parallel with the transmitting terminal p2 A common terminal of (a); the receiving end LCC compensation network further comprises a second receiving end series resonance capacitor C r1 The second receiving terminal is connected in series with a resonant capacitor C r1 One end of the resonant inductor L is connected with the receiving end r The other end of the first receiving end is connected with the series resonance capacitor C of the first receiving end 6 Parallel resonance capacitor C with receiving end r2 To the public terminal.
3. The multi-relay MC-WPT system based on a dual-sided LCC compensation network according to claim 2, wherein the values of the resonance parameters are determined according to the following resonance relations:
wherein, ω is 1 、ω 2 And ω 3 Respectively a transmitting end resonant frequency, a relay resonant frequency and a receiving end resonant frequency.
4. The multi-relay MC-WPT system based on the double-sided LCC compensation network of claim 3, wherein the DC power is provided by an induction power-taking device and a rectifier which are connected with each other, the induction power-taking device takes power from the high voltage transmission line, and then the rectifier rectifies a power source taken by the induction power-taking device and outputs the DC power.
5. The parameter design method of the multi-relay MC-WPT system based on the double-side LCC compensation network is used for the multi-relay MC-WPT system based on the double-side LCC compensation network and is characterized by comprising the following steps of:
s1, determining the DC power supply voltage U according to the actual application scene in System output power P out And a load resistance R L And determining physical parameters of the coupling mechanism according to design requirements;
s2 determining the self-inductance L of the transmitting coil based on the physical parameters of the coupling mechanism 1 And internal resistance R 1 Self-inductance L of N-2 relay coils 2 ,L 3 ,…,L N-1 And a corresponding internal resistance R 2 ,R 3 ,…,R N-1 Self-inductance L of the receiving coil N And internal resistance R N And a coil L i And a coil L j Mutual inductance between M ij I, j ≠ 1,2 ij ＝M ji ；
S3, constructing a (N-1) × (N-1) matrix
And (N-1) × (N-1) matrix
When ω is equal to ω 1 ＝ω 3 Time-sharing receiving end LCC compensation network, high-frequency rectifier and load R L Are commonly equivalent to a resistor
Omega denotes the operating frequency of the high-frequency inverter, the high-frequency rectifier and the load R L Are commonly equivalent to a resistance
S4, determining the resonant frequency omega of the system circuit 0 By passing
Calculating to obtain C 2 ,C 3 ,…,C N-1 Further constructing (N-1) × (N-1) momentsMatrix of
C Ns Is ω ═ ω 1 ＝ω 3 Equivalent capacitance, C, of time-receiving-end LCC compensation network Ns ＝C 2 ＝C 3 ＝…＝C N-1 ；
S5, constructing a matrix polynomial Q (lambda) ═ lambda 2 L s +λR s +C s And 2(N-1) eigenvalues of Q (lambda) are obtained by calculating the spectrum of Q (lambda);
s6, according to the load resistance R L Determining all constant voltage output frequencies and constant current output frequencies in the 2(N-1) characteristic values according to the influence rule of the characteristic value distribution;
s7, determining the optimal constant voltage output frequency and the optimal constant current output frequency according to the magnitude, the attenuation rate and the sensitivity of the system output voltage/current under each constant voltage output frequency and each constant current output frequency;
s8, according to the system design requirement, firstly determining C p2 And C r2 The initial value of (1);
s9, determining values of other resonance parameters according to the optimal constant voltage/constant current output frequency and resonance relation, and adjusting C p2 And C r2 Up to the system output voltage U out Or system output current I out And system output power P out And the design requirement is met.
6. The multi-relay MC-WPT system parameter design method based on the bilateral LCC compensation network as claimed in claim 5, wherein: in step S6, when the load resistance R is lower than the predetermined value L When the output end is short-circuited, the imaginary part of the characteristic value is determined as the constant voltage output frequency; when the load resistance R L When the output end is short-circuited, the imaginary part of the characteristic value is determined as the constant current output frequency.
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