CN113013994A - PT symmetrical SS topology MC-WPT system and implementation method thereof - Google Patents

PT symmetrical SS topology MC-WPT system and implementation method thereof Download PDF

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CN113013994A
CN113013994A CN202110251436.8A CN202110251436A CN113013994A CN 113013994 A CN113013994 A CN 113013994A CN 202110251436 A CN202110251436 A CN 202110251436A CN 113013994 A CN113013994 A CN 113013994A
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coil
symmetrical
electric energy
magnetic coupling
resistance
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CN113013994B (en
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廖志娟
冯其凯
姜陈慧
吴凡
马帅
夏晨阳
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China University of Mining and Technology CUMT
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China University of Mining and Technology CUMT
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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
    • 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
    • H02J50/402—Circuit arrangements or systems for wireless supply or distribution of electric power using two or more transmitting or receiving devices the two or more transmitting or the two or more receiving devices being integrated in the same unit, e.g. power mats with several coils or antennas with several sub-antennas
    • 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
    • H02J50/80—Circuit arrangements or systems for wireless supply or distribution of electric power involving the exchange of data, concerning supply or distribution of electric power, between transmitting devices and receiving devices
    • 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
    • H02J50/90—Circuit arrangements or systems for wireless supply or distribution of electric power involving detection or optimisation of position, e.g. alignment

Abstract

The invention discloses a PT symmetrical SS topology MC-WPT system and an implementation method thereof, wherein PT symmetrical characteristics are applied to a two-coil SS topology magnetic coupling wireless electric energy transmission system which is commonly used at present, and further popularized to a high-order SS topology magnetic coupling wireless electric energy transmission system with any n-coil architecture, wherein,
Figure 150662DEST_PATH_IMAGE001
in time, the two-coil PT symmetrical MC-WPT system is adopted,
Figure 536644DEST_PATH_IMAGE002
the system is a high-order PT symmetrical MC-WPT system with a relay coil. Through the present inventionThe technical scheme of the invention changes the circuit structure of the negative resistance, applies the PT symmetrical characteristic to the SS topology magnetic coupling wireless electric energy transmission system which is most commonly used at present, realizes high-efficiency energy transmission of the SS topology magnetic coupling wireless electric energy transmission system without any external setting, further popularizes the PT symmetrical mechanism to any multi-coil architecture wireless electric energy transmission system, obtains a high-order SS topology magnetic coupling wireless electric energy transmission system, and can effectively improve the transmission distance of the system.

Description

PT symmetrical SS topology MC-WPT system and implementation method thereof
Technical Field
The invention relates to the field of wireless power transmission, in particular to a PT symmetrical SS topology MC-WPT system and an implementation method thereof.
Background
As is well known, currently, a commonly used MC-WPT system can only achieve efficient energy transmission within a specific limited range, once a transmission distance or an azimuth deviates, the energy efficiency of the system decreases sharply, or even decreases with the decrease of the transmission distance, and is limited by spatial transmission performance, such as transmission distance, offset, position robustness, etc., the MC-WPT technology is particularly slow in industrialization process, and effectively improving the spatial transmission performance of the system is a key for promoting the industrial application of the MC-WPT technology.
Regarding the improvement of the spatial energy transfer performance of the MC-WPT system, the improvement of the spatial energy transfer performance to a certain extent is realized by improving the energy efficiency of the system mainly focusing on the aspects of system topology, magnetic coupling mechanisms, electrical parameter optimization design and control and the like at present. However, because the characteristic curve of the system is not changed by the methods, the improvement effect is limited, and the PT symmetrical MC-WPT system can effectively improve the spatial transmission performance of wireless energy transmission.
The space-Time (PT) symmetrical wireless power transmission system can realize high-efficiency energy transmission in a large range without adding any external setting. The current PT symmetrical MC-WPT system implementation modes are two, one is based on an inverter mode, the voltage of an input end is not related to the actual direction of current by controlling the switching frequency of an inverter, and the external characteristic is equivalent to a negative resistance, so that the PT symmetrical system is realized; the other method is to build a negative resistor based on an operational amplifier, construct a PT symmetrical system, and realize high-efficiency energy transfer in a large range under the condition of not increasing any external setting, but the existing implementation mode of the PT symmetrical MC-WPT system has the following defects:
1. in the existing PT symmetric MC-WPT system based on the inverter mode, there is no topological structure limitation, but the frequency of the inverter needs to be controlled, and some additional circuits, such as detection, control or regulation circuits, are added, so that the complexity of the system is increased, and additional loss is also brought.
2. Due to the existence of a virtual pole of a capacitor, a PT symmetrical system based on an operational amplifier mode has the problem that a negative resistor constructed by the operational amplifier is required to be connected with the capacitor in parallel at present, otherwise, the system cannot operate stably. Therefore, the PT symmetric MC-WPT based on the operational amplifier mode cannot be applied to the SS topology, which is the most widely applied topology at present, and thus the application field is limited.
The PT symmetrical system can improve the energy transfer characteristic of the system, but the effective energy transfer distance of the two coil systems is still limited, and the increase of the relay is an effective way for improving the transmission distance, but because the working mode and the corresponding physical principle of the current PT symmetrical mechanism are not completely known, the PT symmetrical system is difficult to popularize and apply to a high-order coil framework, and the PT symmetrical system lacks corresponding parameter design criteria.
Disclosure of Invention
The invention aims to provide a PT symmetrical SS topology MC-WPT system and an implementation method thereof, so as to solve the problems in the prior art.
In order to achieve the purpose, the invention provides the following technical scheme:
a PT symmetrical SS topology MC-WPT system implementation method applies PT symmetrical characteristics to a two-coil SS topology magnetic coupling wireless power transmission system which is commonly used at present and further popularizes the PT symmetrical characteristic to a high-order SS topology magnetic coupling wireless power transmission system of any n-coil architecture, wherein the two-coil PT symmetrical MC-WPT system is adopted when n is 2, and the high-order PT symmetrical MC-WPT system with a relay coil is adopted when n is greater than 2, and is characterized by comprising the following steps of 1 to 4, constructing a transmission parameter model, and determining the PT symmetrical SS topology MC-WPT system of any n-coil architecture by applying the transmission parameter model through the following steps A to C:
step 1, obtaining circuit parameters of each loop corresponding to a circuit in a magnetic coupling wireless power transmission system, wherein the circuit parameters comprise coil self-inductance L and coil equivalent series internal resistance RpA resonance compensation capacitor C and a load resistor RLThen entering step 2;
step 2, combining the obtained circuit parameters of the magnetic coupling wireless electric energy transmission system, respectively determining resistance parameters of an electric energy transmitting end, a relay end and an electric energy receiving end of the magnetic coupling wireless electric energy transmission system, wherein the resistance parameters comprise total gain of the electric energy transmitting end, total resistance of the relay end and total loss of the electric energy receiving end, and then entering step 3;
step 3, respectively aiming at each coil, obtaining the inherent frequency, the characteristic impedance and the attenuation parameter respectively corresponding to each coil according to the circuit parameters obtained in the step 1, the total gain of the electric energy transmitting end and the total loss of the electric energy receiving end obtained in the step 2, combining the structural symmetry condition of the space-time symmetric system to enable the inherent frequency, the characteristic impedance and the attenuation parameter respectively corresponding to each coil to meet the constraint condition, and then entering the step 4;
step 4, solving and obtaining an analytic expression of PT symmetrical parameters of the magnetic coupling wireless power transmission system by combining the circuit parameters obtained in the step 1, the inherent frequency, the characteristic impedance and the attenuation parameters of each coil obtained in the step 3, and characteristic equation expressions and corresponding characteristic value conditions of the magnetic coupling wireless power transmission system, wherein the PT symmetrical parameters comprise singular point parameters, PT symmetrical state parameters and PT symmetrical broken state parameters, so as to obtain a transmission parameter model of the PT symmetrical SS topology MC-WPT system of any n-coil architecture;
step A, according to the method in the steps 1 to 4, obtaining an analytic expression of PT symmetrical parameters of the magnetic coupling wireless power transmission system by applying a transmission parameter model through circuit parameters of each loop in the magnetic coupling wireless power transmission system, a characteristic equation and a characteristic value condition of the circuit, and then entering the step B;
step B, aiming at each coil and each junction in the magnetic coupling wireless electric energy systemDetermining critical coupling coefficient k between adjacent coils of the magnetic coupling wireless power transmission system by combining singular point parameters in PT symmetrical parameters0Determining the maximum critical transmission distance D between adjacent coils of the PT symmetrical system according to the minimum coupling coefficientmaxThen entering step C;
step C, combining the maximum critical transmission distance D between adjacent coils of the magnetic coupling wireless power transmission systemmaxAnd obtaining a PT symmetrical SS topology MC-WPT system with any n-coil architecture according to circuit parameters corresponding to each coil in the magnetic coupling wireless power transmission system and by combining a negative resistance circuit in the magnetic coupling wireless power transmission system.
Preferably, in step 2, the total gain of the power transmitting end, the total resistance of the relay end, and the total loss of the receiving end of the n-coil system are obtained according to the following formulas:
g＝Rg-Rp1
Ri＝Rpi(i＝2,…,n-1)
Rn＝RL+Rpn
wherein g is the total gain of the electric energy transmitting terminal, RgIs a negative resistance, Rp1Is the internal resistance of the transmitting coil, RiIs the total resistance of the ith relay terminal, RpiIs the internal resistance of the i-th relay coil, RnIs the total resistance of the receiving terminal, RLIs a load resistance, RpnIs the internal resistance of the receive coil.
Preferably, in step 3, the natural frequency, the characteristic impedance, and the attenuation parameter respectively corresponding to the system power transmitting end, the power relaying end, and the power receiving end are obtained, according to a formula:
Figure BDA0002966240580000031
Figure BDA0002966240580000032
Figure BDA0002966240580000033
wherein ω is1、ωi、ωnThe natural frequencies, rho, of the coils corresponding to the electric energy transmitting terminal, the ith relay terminal and the electric energy receiving terminal respectively1、ρi、ρnThe characteristic impedance, alpha, of the coil corresponding to the electric energy transmitting terminal, the ith relay terminal and the electric energy receiving terminal respectively1、αnThe attenuation parameters are respectively corresponding to the electric energy transmitting end and the electric energy receiving end.
Preferably, the coil self-inductance L, the resonance compensation capacitance C, and the mutual inductance M between any two adjacent coils of each coil in the magnetic coupling wireless power transmission system satisfy the space-time structural symmetry condition:
Figure BDA0002966240580000041
therefore, the natural frequency, the characteristic impedance and the attenuation parameter of the loop respectively corresponding to the system power transmitting end, the relay end and the receiving end are respectively equal:
Figure BDA0002966240580000042
wherein, ω is0、ρ0、α0Natural frequencies, characteristic impedances, and attenuation parameters equal for each loop of a magnetically coupled wireless power transfer system.
Preferably, the obtaining of the transmission parameters of the high-order magnetic coupling wireless power transmission structure in step 4 includes the following steps:
step 4-1, for a wireless electric energy transmission system with any n-coil framework, obtaining a loop voltage equation, an inductance matrix, a capacitance matrix and a resistance matrix, wherein the loop voltage equation, the inductance matrix, the capacitance matrix and the resistance matrix are respectively as follows:
Figure BDA0002966240580000043
Figure BDA0002966240580000044
wherein U is [ U ]1,u2,...un]TThe system capacitor voltage vector is obtained, L is an inductance matrix, C is a capacitor matrix, and R is a resistance matrix;
step 4-2, combining a loop voltage equation of the magnetic coupling wireless power transmission system to obtain a general expression of a characteristic equation of the magnetic coupling wireless power transmission system with any n-coil architecture, wherein the general expression is as follows:
|-λ2In×n-λ[LC]-1RC-[LC]-1|＝0
wherein, In×nIs an n-order identity matrix, lambda is an eigenvalue of the magnetic coupling wireless power transmission system,
Figure BDA0002966240580000045
wherein k isj,j+1Is the coupling coefficient between any j coil and its adjacent j +1 coil, Mj,j+1Is the mutual inductance between any j-th coil and its adjacent j + 1-th coil, LjCoil self-inductance of the jth coil, Lj+1Is the coil self-inductance of the j +1 th coil, j ═ 1,2, …, n-1;
step 4-3, solving a characteristic equation solution of the magnetic coupling wireless electric energy structure, wherein when the solution of the characteristic value is a real number, the magnetic coupling wireless electric energy transmission system is in a PT symmetrical state, and when the solution of the characteristic value has a plurality of values, the magnetic coupling wireless electric energy transmission system is in a PT symmetrical broken state, a transition point of the magnetic coupling wireless electric energy transmission system from the PT symmetrical state to the PT symmetrical broken state is called a singular point, and the singular point has a value of k0。
Preferably, in the step B, the minimum coupling coefficient between adjacent coils is a singular point k0When the corresponding SS topological system parameter is designed, the coupling coefficient between adjacent coils is always larger than the singular point k0The value of (c).
Preferably, in the step C, when designing the two-coil system, it is ensured that the distance between the transmitting coil and the receiving coil is less than the maximum critical transmission distance, and the total transmission distance of the two-coil system is DmaxWhen any n-coil system is designed, the distance between two adjacent coils is less than the maximum critical transmission distance, and the total transmission distance of the n-coil system is (n-1) Dmax
According to the second aspect of the disclosure, the invention also provides a high-order PT symmetric SS topology MC-WPT system, which includes a negative resistance circuit, a transmitting loop, a relaying loop and a receiving loop;
the negative resistance circuit comprises an operational amplifier and a resistor;
the transmitting loop comprises a transmitting coil self-inductance, a transmitting coil equivalent series resistance and a compensating capacitor of the transmitting loop;
the receiving loop comprises a receiving coil self-inductance, a receiving coil equivalent series resistance, a receiving loop compensation capacitor and a load resistance of the receiving loop;
the relay loop comprises a relay coil self-inductance, a relay coil equivalent series resistance and a relay loop compensation capacitor;
the output of the negative resistance circuit is connected with the negative electrode of the operational amplifier and is connected to the transmitting loop in series, and the resistance value of the negative resistance circuit and the resistance values of all resistors in the negative resistance circuit are determined by combining with the equivalent input resistor in the wireless power transmission system;
and the electric transmitting loop, the relay loop and the receiving loop are coupled through magnetic fields among the coils to carry out energy transmission.
Preferably, the output end of the negative resistance two-terminal network is connected with the negative polarity of the operational amplifier, and the negative resistance circuit comprises a first resistor Rs1A second resistor Rs2And a third resistor R satisfying R between the resistorss2/R＝Rs1/Req。
Preferably, an equivalent input resistance Req ═ R in the wireless power transmission systemp1+Rpn+RLWherein Req is wireless power transmissionEquivalent input resistance, R, of the input systemp1The internal resistance of the coil at the transmitting end of the negative resistance, RpnThe coil internal resistance, R, of the receiving end of the load resistorLIs a load resistor.
Compared with the prior art, the PT symmetrical SS topology MC-WPT system and the implementation method thereof have the following technical effects:
1. the circuit structure of the negative resistance is changed, and the limitation that a negative resistance port constructed based on the traditional operational amplifier is necessarily connected with a capacitor in parallel is broken through;
2. the PT symmetrical characteristic is applied to the most common SS topology magnetic coupling wireless electric energy structure at present, and the SS topology magnetic coupling wireless electric energy transmission system can realize high-efficiency energy transmission without any external setting;
3. the physical principle of the PT symmetrical wireless power transmission system is disclosed, an accurate electrical parameter expression of PT symmetrical parameters is obtained, a PT symmetrical mechanism is popularized to any multi-coil-structure wireless power transmission system, a high-order SS topology magnetic coupling wireless power transmission system is obtained, and the transmission distance of the system can be effectively increased.
Drawings
FIG. 1 is a flowchart of a MC-WPT system implementing a method in accordance with an exemplary embodiment of the present invention;
FIG. 2(a) is a negative resistance circuit diagram of an exemplary embodiment of the present invention, and FIG. 2(b) is a negative resistance equivalent circuit diagram;
fig. 3(a) is a schematic structural diagram of a two-coil system structure according to an exemplary embodiment of the present invention, and fig. 3(b) is an equivalent circuit diagram of the two-coil system structure;
fig. 4(a) is a simulation circuit diagram of a two-coil system configuration according to an exemplary embodiment of the present invention, and fig. 4(b) is a simulation result diagram;
fig. 5(a) is a structural schematic diagram of a three-coil system structure of an exemplary embodiment of the present invention, and fig. 5(b) is a three-coil system structure equivalent circuit diagram;
FIG. 6 is a graph comparing the characteristics of a two coil system and a three coil system in accordance with an exemplary embodiment of the present invention;
fig. 7(a) is a schematic diagram of a structure of an arbitrary coil system structure of an exemplary embodiment of the present invention, and fig. 7(b) is an equivalent circuit diagram of the arbitrary coil system structure.
Detailed Description
In order to better understand the technical content of the present invention, specific embodiments are described below with reference to the accompanying drawings.
In this disclosure, aspects of the present invention are described with reference to the accompanying drawings, in which a number of illustrative embodiments are shown. Embodiments of the present disclosure are not necessarily defined to include all aspects of the invention. It should be appreciated that the various concepts and embodiments described above, as well as those described in greater detail below, may be implemented in any of numerous ways, as the disclosed concepts and embodiments are not limited to any one implementation. In addition, some aspects of the present disclosure may be used alone, or in any suitable combination with other aspects of the present disclosure.
With reference to the flow of the MC-WPT system implementation method in the exemplary embodiment of the present invention shown in fig. 1, based on the existing wireless power transmission system construction method, the present invention applies PT symmetry characteristics to the currently most common SS topology magnetic coupling wireless power structure by changing the circuit structure of the negative resistance, and generalizes a PT symmetry mechanism to any multi-coil architecture wireless power transmission system by revealing the physical principle of the PT symmetric wireless power transmission system, so as to obtain a high-order SS topology magnetic coupling wireless power transmission system, which can effectively increase the transmission distance of the system.
The implementation of the present invention is described in more detail below with reference to fig. 1 to 7.
As shown in fig. 1, a method for implementing a PT symmetric SS topology wireless power transmission system structure applies PT symmetry characteristics to a currently commonly used two-coil SS topology magnetic coupling wireless power transmission system, and further popularizes the PT symmetric SS topology magnetic coupling wireless power transmission system to a high-order SS topology magnetic coupling wireless power transmission system of an arbitrary n-coil architecture, where n is 2, a two-coil PT symmetric MC-WPT system is provided, and when n is greater than 2, a high-order PT symmetric MC-WPT system with a relay coil is provided, the method is characterized by including the following steps 1 to 4 to construct a transmission parameter model, and determining an arbitrary n-coil architecture PT symmetric SS topology MC-WPT system by applying the transmission parameter model through the following steps a to C:
step 1, obtaining circuit parameters of each loop corresponding to a circuit in a magnetic coupling wireless power transmission system, wherein the circuit parameters comprise coil self-inductance L and coil equivalent series internal resistance RpA resonance compensation capacitor C and a load resistor RLThen entering step 2;
step 2, combining the obtained circuit parameters of the magnetic coupling wireless electric energy transmission system, respectively determining resistance parameters of an electric energy transmitting end, a relay end and an electric energy receiving end of the magnetic coupling wireless electric energy transmission system, wherein the resistance parameters comprise total gain of the electric energy transmitting end, total resistance of the relay end and total loss of the electric energy receiving end, and then entering step 3;
step 3, respectively aiming at each coil, obtaining the inherent frequency, the characteristic impedance and the attenuation parameter respectively corresponding to each coil according to the circuit parameters obtained in the step 1, the total gain of the electric energy transmitting end and the total loss of the electric energy receiving end obtained in the step 2, combining the structural symmetry condition of the space-time symmetric system to enable the inherent frequency, the characteristic impedance and the attenuation parameter respectively corresponding to each coil to meet the constraint condition, and then entering the step 4;
step 4, solving and obtaining an analytic expression of PT symmetrical parameters of the magnetic coupling wireless power transmission system by combining the circuit parameters obtained in the step 1, the inherent frequency, the characteristic impedance and the attenuation parameters of each coil obtained in the step 3, and characteristic equation expressions and corresponding characteristic value conditions of the magnetic coupling wireless power transmission system, wherein the PT symmetrical parameters comprise singular point parameters, PT symmetrical state parameters and PT symmetrical broken state parameters, so as to obtain a transmission parameter model of the PT symmetrical SS topology MC-WPT system of any n-coil architecture;
step A, according to the method in the steps 1 to 4, obtaining an analytic expression of PT symmetrical parameters of the magnetic coupling wireless power transmission system by applying a transmission parameter model through circuit parameters of each loop in the magnetic coupling wireless power transmission system, a characteristic equation and a characteristic value condition of the circuit, and then entering the step B;
step B, aiming at each coil in the magnetic coupling wireless electric energy system, determining a critical coupling coefficient k between adjacent coils of the magnetic coupling wireless electric energy transmission system by combining singular point parameters in PT symmetrical parameters0Determining the maximum critical transmission distance D between adjacent coils of the PT symmetrical system according to the minimum coupling coefficientmaxThen entering step C;
step C, combining the maximum critical transmission distance D between adjacent coils of the magnetic coupling wireless power transmission systemmaxAccording to circuit parameters corresponding to each coil in the magnetic coupling wireless power transmission system and a negative resistance circuit in the magnetic coupling wireless power transmission system, a high-order PT symmetrical SS topology MC-WPT system of any n-coil architecture is obtained.
Preferably, with reference to fig. 2 to 4, a two-coil SS topology PT symmetric wireless power transmission system structure is selected, which specifically includes:
step 1, obtaining circuit parameters of each loop corresponding to a circuit in a magnetic coupling wireless power transmission system, wherein the circuit parameters comprise coil self-inductance L and coil equivalent series internal resistance RpA resonance compensation capacitor C and a load resistor RLThen entering step 2;
step 2, combining the obtained circuit parameters of the magnetic coupling wireless electric energy transmission system, respectively determining resistance parameters of an electric energy transmitting end and an electric energy receiving end of the magnetic coupling wireless electric energy transmission system, wherein the resistance parameters comprise total gain of the electric energy transmitting end and total loss of the electric energy receiving end, and determining a negative resistance value in the magnetic coupling wireless electric energy structure and resistance values of resistors in coils corresponding to the negative resistance:
g＝Rg-Rp1
R2＝RL+Rp2
wherein g is the total gain of the electric energy transmitting terminal, RgIs a negative resistance, Rp1Is the internal resistance of the transmitting coil, R2Is the total resistance of the receiving terminal, RLIs a load resistance, Rp2For receiving the internal resistance of the coil, a first coil is included in the coil corresponding to the power transmitting endResistance Rs1A second resistor Rs2And a third resistor R satisfying R between the resistorss2/R＝Rs1(Req), equivalent input resistance Req ═ R in wireless power transmission systemp1+Rp2+RLWherein Req is the equivalent input resistance, Rp1Internal resistance of the coil corresponding to the transmitting loop in which the negative resistance is located, Rp2The internal resistance, R, of the coil corresponding to the power receiving terminal at which the load resistor is locatedLTo load resistance, then go to step 3;
and 3, respectively aiming at each coil, obtaining the inherent frequency, the characteristic impedance and the attenuation parameter respectively corresponding to each coil according to the circuit parameters obtained in the step 1, the total gain of the electric energy transmitting end and the total loss of the electric energy receiving end obtained in the step 2:
Figure BDA0002966240580000081
Figure BDA0002966240580000091
Figure BDA0002966240580000092
wherein ω is1、ω2The natural frequencies, rho, of the coils corresponding to the electric energy transmitting end and the electric energy receiving end respectively1、ρ2Characteristic impedance, alpha, of the corresponding coils of the electric energy transmitting terminal and the electric energy receiving terminal respectively1、α2Attenuation parameters corresponding to the electric energy transmitting end and the electric energy receiving end are respectively set;
meanwhile, the coil self-inductance L, the resonance compensation capacitance C and the mutual inductance M between any two adjacent coils of each coil in the magnetic coupling wireless power transmission system meet the space-time structural symmetry condition:
Figure BDA0002966240580000093
therefore, the natural frequency, the characteristic impedance and the attenuation parameter of the corresponding loop of the system electric energy transmitting end and the receiving end are respectively equal:
Figure BDA0002966240580000094
wherein, ω is0、ρ0、α0Natural frequencies, characteristic impedances, and attenuation parameters equal for each loop of a magnetically coupled wireless power transfer system. Then entering step 4;
step 4, solving and obtaining an analytic expression of PT symmetrical parameters of the magnetic coupling wireless power transmission system by combining the circuit parameters obtained in the step 1, the natural frequency, the characteristic impedance and the attenuation parameters of each coil obtained in the step 3, and the characteristic equation expressions and the corresponding characteristic value conditions of the magnetic coupling wireless power transmission system, wherein the PT symmetrical parameters comprise singular point parameters, PT symmetrical state parameters and PT symmetrical default state parameters, so as to obtain a transmission parameter model of the PT symmetrical SS topology MC-WPT system of the two-coil framework, and the method comprises the following steps:
step 4-1, for a wireless electric energy transmission system with two coil structures, obtaining a loop voltage equation, an inductance matrix, a capacitance matrix and a resistance matrix, wherein the loop voltage equation, the inductance matrix, the capacitance matrix and the resistance matrix are respectively as follows:
Figure BDA0002966240580000095
Figure BDA0002966240580000096
wherein U is [ U ]1,u2]TThe system capacitor voltage vector is obtained, L is an inductance matrix, C is a capacitor matrix, and R is a resistance matrix;
step 4-2, combining a loop voltage equation of the magnetic coupling wireless electric energy transmission system to obtain a general expression of a characteristic equation of the magnetic coupling wireless electric energy transmission system of the two coil framework systems, wherein the general expression is as follows:
|-λ2I2×2-λ[LC]-1RC-[LC]-1|＝0
wherein, I2×2The method is a 2-order unit matrix, lambda is an eigenvalue of the magnetic coupling wireless power transmission system, a general expression of a characteristic equation is simplified, the simplified characteristic equation of the magnetic coupling wireless power transmission system is obtained, and the characteristic equation is as follows:
(1-k2)λ4-(2-α0 2)ω0 2λ2+ω0 4＝0
wherein k is a coupling coefficient between two coils in the magnetic coupling wireless power transmission system;
step 4-3, solving a characteristic equation solution of the magnetic coupling wireless electric energy structure, wherein when the solution of the characteristic value is a real number, the magnetic coupling wireless electric energy transmission system is in a PT symmetrical state, and when the solution of the characteristic value has a plurality of values, the magnetic coupling wireless electric energy transmission system is in a PT symmetrical broken state, a transition point of the magnetic coupling wireless electric energy transmission system from the PT symmetrical state to the PT symmetrical broken state is called a singular point, and the singular point has a value of k0，
Figure BDA0002966240580000101
Step A, according to the method in the step 1 to the step 4, obtaining an analytic expression of PT symmetrical parameters of the magnetic coupling wireless power transmission system by applying a transmission parameter model through circuit parameters of each loop in the magnetic coupling wireless power transmission system, and characteristic equations and characteristic value conditions of the circuits, and then entering the step B;
step B, for each coil in the magnetic coupling wireless electric energy system, determining a critical coupling coefficient k of the magnetic coupling wireless electric energy transmission system by combining singular point parameters in PT symmetrical parameters0Determining the maximum critical transmission distance D of the PT symmetrical system according to the minimum coupling coefficientmaxThe minimum coupling coefficient between the coils is a singular point k0Coupling between coils in the case of corresponding SS topology parameter designThe sum coefficient is always greater than the singular point k0Then step C is entered;
step C, combining the maximum critical transmission distance D of the magnetic coupling wireless power transmission systemmaxAccording to circuit parameters corresponding to each coil in the magnetic coupling wireless power transmission system and by combining a negative resistance circuit in the magnetic coupling wireless power transmission system, a PT symmetrical SS topology MC-WPT system with a two-coil structure is obtained, and the distance between a transmitting coil and a receiving coil is smaller than the maximum critical transmission distance Dmax。
The two-coil system is simulated, a simulation model shown in fig. 4(a) is built by using PSIM software, and stable sine wave voltage output by the negative resistance circuit can be obtained as shown in fig. 4 (b). Therefore, by combining the parameter design criteria of the negative resistance circuit and the two-coil PT symmetrical system, the obtained two-coil PT symmetrical SS topological system can realize stable self-oscillation without external setting, thereby realizing high-efficiency energy transfer.
Preferably, referring to fig. 5, when n is 3, the system is a three-coil PT symmetric SS topology MC-WPT system, and the total resistance, R, of the relay terminal needs to be determined in step 2i＝Rpi(i＝2)；
The natural frequency, the characteristic impedance and the attenuation parameter corresponding to the electric energy relay terminal are determined according to the formula:
Figure BDA0002966240580000111
ω2is the natural frequency of the relay coil, p2Is the characteristic impedance of the relay coil;
the coil self-inductance L, the resonance compensation capacitance C and the mutual inductance M between any two adjacent coils of each coil in the magnetic coupling wireless power transmission system meet the space-time structural symmetry condition:
Figure BDA0002966240580000112
therefore, the natural frequency, the characteristic impedance and the attenuation parameter of the loop respectively corresponding to the system power transmitting end, the relay end and the receiving end are respectively equal:
Figure BDA0002966240580000113
wherein, ω is0、ρ0、α0The natural frequency, the characteristic impedance and the attenuation parameter which are equal to each loop of the magnetic coupling wireless power transmission system;
obtaining transmission parameters of the high-order magnetic coupling wireless power transmission structure in step 4, comprising the following steps:
step 4-1, for a wireless electric energy transmission system with a three-coil framework, obtaining a loop voltage equation, an inductance matrix, a capacitance matrix and a resistance matrix, wherein the loop voltage equation, the inductance matrix, the capacitance matrix and the resistance matrix are respectively as follows:
Figure BDA0002966240580000114
Figure BDA0002966240580000115
wherein U is [ U ]1,u2,u3]TThe system capacitor voltage vector is obtained, L is an inductance matrix, C is a capacitor matrix, and R is a resistance matrix;
step 4-2, combining a loop voltage equation of the magnetic coupling wireless power transmission system to obtain a general expression of a characteristic equation of the magnetic coupling wireless power transmission system with any n-coil architecture, wherein the general expression is as follows:
|-λ2I3×3-λ[LC]-1RC-[LC]-1|＝0
wherein, I3×3The method is a 3-order unit matrix, lambda is an eigenvalue of the magnetic coupling wireless power transmission system, a general expression of a characteristic equation is simplified, and the characteristic equation of the magnetic coupling wireless power transmission system is obtained, wherein the characteristic equation is as follows:
(1-2k2)λ4-(2-α0 2)ω0 2λ2+ω0 4＝0
wherein k is a coupling coefficient between two adjacent coils in the magnetic coupling wireless power transmission system,
Figure BDA0002966240580000121
wherein k isj,j+1Is the coupling coefficient between any j coil and its adjacent j +1 coil, Mj,j+1Is the mutual inductance between any j-th coil and its adjacent j + 1-th coil, LjCoil self-inductance of the jth coil, Lj+1Is the coil self-inductance of the j +1 th coil, j ═ 1,2, …, n-1;
step 4-3, solving a characteristic equation solution of the magnetic coupling wireless electric energy structure, wherein when the solution of the characteristic value is a real number, the magnetic coupling wireless electric energy transmission system is in a PT symmetrical state, and when the solution of the characteristic value has a plurality of values, the magnetic coupling wireless electric energy transmission system is in a PT symmetrical broken state, a transition point of the magnetic coupling wireless electric energy transmission system from the PT symmetrical state to the PT symmetrical broken state is called a singular point, and the singular point has a value of k0，
Figure BDA0002966240580000122
Maximum critical transmission distance D between adjacent coils of wireless power transmission system combined with magnetic couplingmaxAccording to circuit parameters corresponding to each coil in the magnetic coupling wireless power transmission system and by combining a negative resistance circuit in the magnetic coupling wireless power transmission system, a high-order PT symmetrical SS topology MC-WPT system with a three-coil structure is obtained, the distance between two adjacent coils is smaller than the maximum critical transmission distance, and the total transmission distance of the three-coil system is 2Dmax。
In order to confirm that the three-coil PT symmetric system can greatly improve the transmission distance of the system for high-efficiency energy transmission, MATLAB software is used for respectively carrying out simulation verification on the energy efficiency characteristics of the two-coil system and the three-coil system, the simulation result is shown in FIG. 6, and the singular point of the two-coil system is k1(corresponding system transmission)A distance D1) And the singular point of the three-coil system is k2(corresponding to a total transmission distance of the system of 2D2). Therefore, through comparative analysis, the transmission distance of the three-coil system is improved by more than two times under the condition that the transmission efficiency is not changed.
In an alternative embodiment, in conjunction with fig. 3-7, the present invention may also be configured to be implemented as follows:
a high-order PT symmetrical SS topology MC-WPT system comprises a negative resistance circuit, a transmitting loop, a relay loop and a receiving loop;
the negative resistance circuit comprises an operational amplifier and a resistor;
the transmitting loop comprises a transmitting coil self-inductance, a transmitting coil equivalent series resistance and a compensating capacitor of the transmitting loop;
the receiving loop comprises a receiving coil self-inductance, a receiving coil equivalent series resistance, a receiving loop compensation capacitor and a load resistance of the receiving loop;
the relay loop comprises a relay coil self-inductance, a relay coil equivalent series resistance and a relay loop compensation capacitor;
the output of the negative resistance circuit is connected with the negative electrode of the operational amplifier and is connected to the transmitting loop in series, and the resistance value of the negative resistance circuit and the resistance values of all resistors in the negative resistance circuit are determined by combining with the equivalent input resistor in the wireless power transmission system;
the electric transmitting loop, the relay loop and the receiving loop are coupled through magnetic fields among coils to carry out energy transmission;
preferably, the two-coil PT symmetrical SS topology MC-WPT system comprises only a negative resistance circuit, a transmitting loop and a receiving loop, and the n-coil PT symmetrical SS topology MC-WPT system comprises n-2 relay terminals, as shown in FIG. 7.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to be limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, the protection scope of the present invention should be determined by the appended claims.

Claims (10)

1. A PT symmetrical SS topology MC-WPT system implementation method applies PT symmetrical characteristics to a two-coil SS topology magnetic coupling wireless power transmission system which is commonly used at present and further popularizes the PT symmetrical characteristic to a high-order SS topology magnetic coupling wireless power transmission system of any n-coil architecture, wherein the two-coil PT symmetrical MC-WPT system is adopted when n is 2, and the high-order PT symmetrical MC-WPT system with a relay coil is adopted when n is greater than 2, and is characterized by comprising the following steps of 1 to 4, constructing a transmission parameter model, and determining the PT symmetrical SS topology MC-WPT system of any n-coil architecture by applying the transmission parameter model through the following steps A to C:
step 1, obtaining circuit parameters of each loop corresponding to a circuit in a magnetic coupling wireless power transmission system, wherein the circuit parameters comprise coil self-inductance L and coil equivalent series internal resistance RpA resonance compensation capacitor C and a load resistor RLThen entering step 2;
step 2, combining the obtained circuit parameters of the magnetic coupling wireless electric energy transmission system, respectively determining resistance parameters of an electric energy transmitting end, a relay end and an electric energy receiving end of the magnetic coupling wireless electric energy transmission system, wherein the resistance parameters comprise total gain of the electric energy transmitting end, total resistance of the relay end and total loss of the electric energy receiving end, and then entering step 3;
step 3, respectively aiming at each coil, obtaining the inherent frequency, the characteristic impedance and the attenuation parameter respectively corresponding to each coil according to the circuit parameters obtained in the step 1, the total gain of the electric energy transmitting end and the total loss of the electric energy receiving end obtained in the step 2, combining the structural symmetry condition of the space-time symmetric system to enable the inherent frequency, the characteristic impedance and the attenuation parameter respectively corresponding to each coil to meet the constraint condition, and then entering the step 4;
step 4, solving to obtain an analytical expression of PT symmetrical parameters of the magnetic coupling wireless power transmission system by combining the circuit parameters obtained in the step 1, the inherent frequency, the characteristic impedance and the attenuation parameters of each coil obtained in the step 3, and a characteristic equation expression and corresponding characteristic value conditions of the magnetic coupling wireless power transmission system, wherein the PT symmetrical parameters comprise singular point parameters, PT symmetrical state parameters and PT symmetrical broken state parameters, so as to obtain a transmission parameter model of the PT symmetrical SS topology MC-WPT system of any n-coil architecture;
step A, according to the method in the steps 1 to 4, obtaining an analytic expression of PT symmetrical parameters of the magnetic coupling wireless power transmission system by applying a transmission parameter model through circuit parameters of each loop in the magnetic coupling wireless power transmission system, a characteristic equation and a characteristic value condition of the circuit, and then entering the step B;
step B, aiming at each coil in the magnetic coupling wireless electric energy system, determining a critical coupling coefficient k between adjacent coils of the magnetic coupling wireless electric energy transmission system by combining singular point parameters in PT symmetrical parameters0According to the critical coupling coefficient k0Determining the maximum critical transmission distance D between adjacent coils of the systemmaxThen entering step C;
step C, combining the maximum critical transmission distance D between adjacent coils of the magnetic coupling wireless power transmission systemmaxAccording to circuit parameters corresponding to each coil in the magnetic coupling wireless power transmission system and a negative resistance circuit in the magnetic coupling wireless power transmission system, a high-order PT symmetrical SS topology MC-WPT system of any n-coil architecture is obtained.
2. The method for implementing the PT symmetrical SS topology MC-WPT system as claimed in claim 1, wherein in the step 2, the total gain of the power transmitting end, the total resistance of the relay end, and the total loss of the receiving end of any n-coil system are obtained according to the following formulas:
g＝Rg-Rp1
Ri＝Rpi(i＝2,…,n-1)
Rn＝RL+Rpn
wherein g is the total gain of the electric energy transmitting terminal, RgIs the resistance value of a negative resistance, Rp1Is the internal resistance of the transmitting coil, RiIs the ithTotal resistance of relay terminal, RpiIs the internal resistance of the i-th relay coil, RnIs the total resistance of the receiving terminal, RLIs a load resistance, RpnIs the internal resistance of the receive coil.
3. The method for implementing the PT symmetrical SS topology MC-WPT system according to claim 1 or 2, wherein in the step 3, the inherent frequency, the characteristic impedance and the attenuation parameter respectively corresponding to the system electric energy transmitting terminal, the electric energy relay terminal and the electric energy receiving terminal are obtained, according to a formula:
Figure FDA0002966240570000021
Figure FDA0002966240570000022
Figure FDA0002966240570000023
wherein ω is1、ωi、ωnThe natural resonant frequencies, rho, of the coils corresponding to the electric energy transmitting end, the ith relay end and the electric energy receiving end respectively1、ρi、ρnThe characteristic impedance, alpha, of the coil corresponding to the electric energy transmitting terminal, the ith relay terminal and the electric energy receiving terminal respectively1、αnThe attenuation parameters are respectively corresponding to the electric energy transmitting end and the electric energy receiving end.
4. The implementation method of the PT symmetrical SS topology MC-WPT system as claimed in claim 3, wherein the coil self-inductance L, the resonance compensation capacitance C and the mutual inductance M between any two adjacent coils of each coil in the magnetic coupling wireless power transmission system satisfy the space-time structural symmetry condition:
Figure FDA0002966240570000024
therefore, the natural frequency, the characteristic impedance and the attenuation parameter of the loop respectively corresponding to the system power transmitting end, the relay end and the receiving end are respectively equal:
Figure FDA0002966240570000031
wherein, ω is0、ρ0、α0Natural frequencies, characteristic impedances, and attenuation parameters equal for each loop of a magnetically coupled wireless power transfer system.
5. The method for implementing the PT-symmetrical SS topology MC-WPT system according to claim 4, wherein the obtaining of the transmission parameters of the high-order magnetic coupling wireless power transmission structure in the step 4 includes the following steps:
step 4-1, for a wireless electric energy transmission system with any n-coil framework, obtaining a loop voltage equation, an inductance matrix, a capacitance matrix and a resistance matrix, wherein the loop voltage equation, the inductance matrix, the capacitance matrix and the resistance matrix are respectively as follows:
Figure FDA0002966240570000032
Figure FDA0002966240570000033
wherein U is [ U ]1,u2,...un]TThe system capacitor voltage vector is obtained, L is an inductance matrix, C is a capacitor matrix, and R is a resistance matrix;
step 4-2, combining a loop voltage equation of the magnetic coupling wireless power transmission system to obtain a general expression of a characteristic equation of the magnetic coupling wireless power transmission system with any n-coil architecture, wherein the general expression is as follows:
|-λ2In×n-λ[LC]-1RC-[LC]-1|＝0
wherein, In×nIs an n-order identity matrix, and lambda is an eigenvalue of a magnetic coupling wireless power transmission system
Figure FDA0002966240570000034
Wherein k isj,j+1Is the coupling coefficient between any j coil and its adjacent j +1 coil, Mj,j+1Is the mutual inductance between any j-th coil and its adjacent j + 1-th coil, LjCoil self-inductance of the jth coil, Lj+1Is the coil self-inductance of the j +1 th coil, j ═ 1,2, …, n-1;
step 4-3, solving a characteristic equation solution of the magnetic coupling wireless electric energy structure, wherein when the solution of the characteristic value is a real number, the magnetic coupling wireless electric energy transmission system is in a PT symmetrical state, and when the solution of the characteristic value has a plurality of values, the magnetic coupling wireless electric energy transmission system is in a PT symmetrical broken state, a transition point of the magnetic coupling wireless electric energy transmission system from the PT symmetrical state to the PT symmetrical broken state is called a singular point, and the singular point has a value of k0。
6. The implementation method of the PT-symmetrical SS topology MC-WPT system as claimed in claim 1, wherein in the step B, the minimum coupling coefficient between adjacent coils is a singular point k0When the corresponding SS topological system parameter design is carried out, the coupling coefficient between adjacent coils is always larger than the singular point k0The value of (c).
7. The method as claimed in claim 1, wherein in step C, the distance between the transmitting coil and the receiving coil is ensured to be less than the maximum critical transmission distance when the two-coil system is designed, and the total transmission distance of the two-coil system is DmaxWhen any n-coil system is designed, the distance between two adjacent coils is less than the maximum critical transmission distance, and the total transmission distance of the n-coil system is (n-1) Dmax。
8. A high-order PT symmetrical SS topology MC-WPT system is characterized by comprising a negative resistance circuit, a transmitting loop, a relay loop and a receiving loop;
the negative resistance circuit comprises an operational amplifier and a resistor;
the transmitting loop comprises a transmitting coil self-inductance, a transmitting coil equivalent series resistance and a compensating capacitor of the transmitting loop;
the receiving loop comprises a receiving coil self-inductance, a receiving coil equivalent series resistance, a receiving loop compensation capacitor and a load resistance of the receiving loop;
the relay loop comprises a relay coil self-inductance, a relay coil equivalent series resistance and a relay loop compensation capacitor;
the output of the negative resistance circuit is connected with the negative electrode of the operational amplifier and is connected to the transmitting loop in series, and the resistance value of the negative resistance circuit and the resistance values of all resistors in the negative resistance circuit are determined by combining with the equivalent input resistor in the wireless power transmission system;
and the electric transmitting loop, the relay loop and the receiving loop are coupled through magnetic fields among the coils to carry out energy transmission.
9. The MC-WPT system with high-order PT symmetrical SS topology according to claim 8, wherein the negative resistance two-terminal network output terminal is connected with the negative polarity terminal of the operational amplifier, and the negative resistance circuit comprises a first resistor Rs1A second resistor Rs2And a third resistor R satisfying R between the resistorss2/R＝Rs1/Req。
10. The MC-WPT system with higher-order PT symmetrical SS topology according to claim 9, wherein equivalent input resistance Req R in the wireless power transmission systemp1+Rpn+RLWherein Req is equivalent input resistance of the wireless power transmission system, Rp1The internal resistance of the coil at the transmitting end of the negative resistance, RpnTo load electricityInternal resistance of the coil at the receiving end, RLIs a load resistor.
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