CN109638977B - Stereoscopic space multi-node power balancing wireless power supply system and method - Google Patents

Stereoscopic space multi-node power balancing wireless power supply system and method Download PDF

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CN109638977B
CN109638977B CN201910074588.8A CN201910074588A CN109638977B CN 109638977 B CN109638977 B CN 109638977B CN 201910074588 A CN201910074588 A CN 201910074588A CN 109638977 B CN109638977 B CN 109638977B
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CN109638977A (en
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闻枫
李强
李睿
刘力
顾伟
云珂
李宇逍
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Nanjing University of Science and Technology
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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
    • H02J50/50—Circuit arrangements or systems for wireless supply or distribution of electric power using additional energy repeaters between transmitting devices and receiving devices
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02T90/10—Technologies relating to charging of electric vehicles
    • Y02T90/14—Plug-in electric vehicles

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Abstract

The invention discloses a three-dimensional multi-node power balance wireless power supply system and a method, aiming at a system with a disc-type spiral structure, a transmitting coil is arranged below a receiving coil at the same height in a three-dimensional space, so that the receiving coil at the same height is symmetrically positioned around the axis of the corresponding transmitting coil; among the transmitting coils with different heights, only the transmitting coil at the bottommost layer is electrified, and the rest transmitting coils are used as relay transmitting coils and are not electrified. When power is supplied, firstly, establishing a corresponding relation of mutual inductance between the transmitting coil and the relay transmitting coil along with distance change; determining a limiting condition of mutual inductance values between the transmitting coil and the relay transmitting coil when the receiving powers of all the loads are equal; and then, weakening or enhancing loop resistance of the transmitting coil and the relay transmitting coil to adjust the mutual inductance value between the two coils meeting the limited condition, so that the mutual inductance value accords with the corresponding relation with the distance between the two coils, and power balance wireless power supply is realized. The invention overcomes the defect of overlarge current at the power supply end during power balance.

Description

Stereoscopic space multi-node power balance wireless power supply system and method
Technical Field
The invention relates to a wireless power transmission technology, in particular to a three-dimensional multi-node power balancing wireless power supply system and a method.
Background
The direct contact of the conducting wires is the main mode of electric energy transmission, but the mode inevitably generates transmission loss, and meanwhile, factors such as line aging, point discharge and the like also easily cause electric sparks, so that the reliability and the safety of power supply of equipment are greatly reduced. The wireless charging technology can solve the charging infrastructure limitation and the above safety problem faced by the traditional charging, and has attracted the great attention of researchers. In order to further improve the utilization rate of wireless charging, people assume various three-dimensional multi-node power supply systems, such as a wireless charging system of an electric vehicle in a multi-layer three-dimensional garage, a wireless charging system of Wireless Sensor Network (WSNs) node devices, a wireless charging system of supermarket multi-layer shelf electronic labels (ESLs), and the like. Increasing the current passed through the transmitting coil can keep the multi-load power balance of each layer, but the requirement on the current provided by the front-end driving power supply is high, and the implementation is difficult.
Disclosure of Invention
The invention aims to provide a stereoscopic space multi-node power balance wireless power supply system and method.
The technical solution for realizing the purpose of the invention is as follows: a three-dimensional space multi-node power balance wireless power supply system aims at a wireless power supply system with a disc-type spiral structure, a transmitting coil is arranged below a receiving coil at the same height in a three-dimensional space, so that the receiving coil at the same height is symmetrically positioned around the axis of the corresponding transmitting coil; among the transmitting coils of different heights, only the transmitting coil of the bottommost layer is electrified, and the rest serving as relay transmitting coils are not electrified.
As a preferred embodiment, the transmitting coils of each layer are of uniform size.
As a preferred embodiment, the number and size of the receiving coils of each layer are uniform.
A stereoscopic space multi-node power balancing wireless power supply method comprises the following steps:
step 1, establishing a corresponding relation of mutual inductance between a transmitting coil and a relay transmitting coil along with distance change according to coil parameters;
step 2, determining a limiting condition of mutual inductance values between the transmitting coil and the relay transmitting coil when the receiving powers of all the loads are equal;
and 3, weakening or enhancing loop resistance of the transmitting coil and the relay transmitting coil to adjust the mutual inductance value between the two coils meeting the limited condition, so that the mutual inductance value accords with the corresponding relation of the distance between the two coils, and power balance wireless power supply is realized.
As a preferred embodiment, in the case of a double-layer load, in step 1, the mutual inductance and the distance between the transmitting coil and the relay transmitting coil satisfy the following relationship:
Figure GDA0003759769520000021
in the formula, Ψ 21 Representing the flux linkage, Φ, through the transmitting coil TX1 and the relay transmitting coil TX2 sn Representing the magnetic flux of the n-th turn of the relay transmitter coil, M 12 And M 21 Representing the mutual inductance between the transmitter coil and the relay transmitter coil, I TX1 Representing the current through the transmitting coil, mu 0 Denotes the vacuum permeability, n 1 And n 2 The number of turns of the transmitting coil and the relay transmitting coil are respectively indicated, d and d 1 Respectively representing the turn-to-turn distance of the transmitting coil and the relay transmitting coil, wherein the outer radius of the transmitting coil is R, the inner radius of the relay transmitting coil is R ', and the radius R of the relay transmitting coil ranges from 0 to R' + (j-1) d 1 H represents the distance between the relay transmitting coil and the transmitting coil, phi represents an angle, and has no practical significance.
As a more preferred embodiment, in step 2, neglecting the mutual influence between the receiving coils, and the influence of the transmitting coil or the relay transmitting coil of a different layer on the receiving coil, respectively writing KVL equation for the first layer transmitting coil, the second layer relay transmitting coil, and the second layer receiving coil:
Figure GDA0003759769520000022
in the formula (I), the compound is shown in the specification,
Figure GDA0003759769520000023
representing the input voltage, omega is the angular frequency, m and n represent the number of receiving coils of the first layer and the second layer respectively,
Figure GDA0003759769520000024
and
Figure GDA0003759769520000025
respectively representing the passage in all the receiving coils of the first layer and all the receiving coils of the second layerCurrent of R TX1 And R TX2 Respectively representing the internal resistance, R, of the first layer transmitting coil and the second layer relay transmitting coil a1 And R b1 Respectively representing the internal resistance values, M, of the first receiving coil of the first layer and the first receiving coil of the second layer 1a1 Representing the mutual inductance, M, between the transmitter coil of the first layer and the first receiver coil of the first layer 2b1 Representing the mutual inductance, M, between the second layer relay transmitter coil and the second layer first receiver coil 12 And M 21 Representing the mutual inductance, M, between the first layer transmitter coil and the second layer relay transmitter coil 21 Representing a mutual inductance value between the second layer relay transmitter coil and the first layer transmitter coil;
solving the expressions of the current passing through the transmitting coil TX1 and the current passing through the receiving coil of the first layer, and the current passing through the relay transmitting coil TX2 of the second layer and the current passing through the receiving coil of the second layer as follows:
Figure GDA0003759769520000031
when the sizes of the transmitting coil and the relay transmitting coil are completely consistent and the size of the receiving coil design of each layer is completely consistent, the following four conditions are met: 1) the resistance of the loops of the receiving coils on different layers is equal, 2) the resistance of the loops of the transmitting coil and the relay transmitting coil is equal, 3) the mutual inductance value of the transmitting coil or the relay transmitting coil and the receiving coil on the same layer is equal to that of other layers, 4) the number of the receiving coils on each layer is the same, namely:
Figure GDA0003759769520000032
in order to equalize the received power of all loads, i.e. the current I passed by the receiving coil of the first layer RX1 And the second layer receives the current I passing through the coil RX2 The constraint condition for deriving the mutual inductance values is as follows:
Figure GDA0003759769520000033
as a most preferred embodiment, in step 3, the loop resistances of the transmitting coil and the relay transmitting coil are weakened or strengthened by using series-parallel resistances or impedance matching networks, etc., so as to adjust the mutual inductance value between the two coils meeting the defined condition, so that the mutual inductance value conforms to the corresponding relationship with the coil pitch.
Compared with the prior art, the invention has the following remarkable advantages: according to the invention, by weakening or enhancing the loop resistance of the transmitting coil and the relay transmitting coil, when the distance between the transmitting coil and the relay transmitting coil is changed, the current passing through each layer of receiving coil is still kept equal, the multi-node output power balance in a three-dimensional space is ensured, and the defect of large current passing through a power supply end is overcome.
Drawings
Fig. 1 is a flow chart of an implementation of a wireless power supply scheme with spatial multi-node power balancing according to the present invention.
Fig. 2 is a structural diagram of a coupling mechanism of a multi-layer three-dimensional wireless power transmission system according to the present invention.
Fig. 3 is an equivalent circuit diagram corresponding to the structure diagram of the coupling mechanism of the multi-layer three-dimensional wireless power transmission system.
FIG. 4 is a graph showing the mutual inductance between coils according to the present invention as a function of distance.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings.
The invention relates to a three-dimensional space multi-node power balance wireless power supply system which is suitable for the condition of a disc-type spiral structure.A transmitting coil is arranged under a receiving coil which is close to the receiving coil at the same height in a three-dimensional space, so that the receiving coils at the same height are symmetrically positioned around the axis of the corresponding transmitting coil; among the transmitting coils of different heights, only the transmitting coil of the bottommost layer is electrified, and the rest transmitting coils are not electrified as relay transmitting coils.
When power balance wireless power supply is carried out on the system, firstly, a three-dimensional space multi-node wireless power supply system model is built; then, according to the coil parameters, establishing a corresponding relation of mutual inductance between the transmitting coil and the relay transmitting coil along with the change of the distance; determining a limiting condition of mutual inductance values between the transmitting coil and the relay transmitting coil when the receiving powers of all the loads are equal; finally, the loop resistance of the transmitting coil and the relay transmitting coil is weakened or enhanced by means of series-parallel resistors or impedance matching networks and the like, so that the mutual inductance value between the two coils meeting the limiting conditions is adjusted to be in accordance with the corresponding relation of the distance between the two coils, the current passing through each layer of receiving coil is ensured to be equal, and power balance wireless power supply is realized.
To facilitate an understanding of the inventive solution, the following is a description of the relevant theory of keeping the output power constant.
Fig. 2 shows an example of a structure of a coupling mechanism of a wireless power transmission system, in which a self-resonant relay transmitter coil is disposed closely under a receiver coil when the receiver coil is located at different heights in a three-dimensional space. The first layer serves as a transmission coil TX1, and the second layer TX2 through the k-th layer TXk serve as relay transmission coils. A certain number of receiving coils RX are symmetrically placed on each layer of coils, for example, the number of receiving coils RX1 on the first layer is m; the number of the receiving coils of the second layer is n, and RX2 is adopted; the number of the receiving coils of the k-th layer is RXk, and p. By reasonably configuring system parameters, all receiving coils in the space can obtain the same energy.
According to the structure diagram of the coupling mechanism of the multi-layer three-dimensional space wireless power transmission system in fig. 2, a corresponding equivalent circuit diagram can be obtained as shown in fig. 3. Neglecting the mutual influence among the receiving coils and the influence of the transmitting coils or the relay transmitting coils of different layers on the receiving coils, respectively writing the KVL equation for the transmitting coil of the first layer, the relay transmitting coil of each layer and the receiving coil as follows:
Figure GDA0003759769520000051
in the formula
Figure GDA0003759769520000052
Representing the input voltage, omega is the angular frequency,
Figure GDA0003759769520000053
Figure GDA0003759769520000054
and
Figure GDA0003759769520000055
respectively representing the current passing through a transmitting coil, a first layer first receiving coil, a first layer mth receiving coil, a second layer relay transmitting coil, a second layer first receiving coil, a second layer nth receiving coil, a k layer relay transmitting coil, a k layer first receiving coil, a k layer pth receiving coil and a k-1 layer relay transmitting coil; r TX1 、R TX2 And R TXk Respectively representing the internal resistance values of the first layer transmitting coil, the second layer relay transmitting coil and the k layer relay transmitting coil; l is a radical of an alcohol TX1 、L TX2 And L TXk Respectively representing self-inductance values of a first layer transmitting coil, a second layer relay transmitting coil and a k layer relay transmitting coil; c TX1 、C TX2 And C TXk Respectively representing the capacitance values of the series resonance capacitors of the first layer transmitting coil, the second layer relay transmitting coil and the k layer relay transmitting coil; r a1 、R b1 And R k1 Respectively representing the internal resistance values of a first receiving coil of a first layer, a first receiving coil of a second layer and a first receiving coil of a k-th layer; l is a1 、L b1 And L k1 Respectively representing self-inductance values of a first receiving coil of a first layer, a first receiving coil of a second layer and a first receiving coil of a k-th layer; c a1 、C b1 And C k1 Respectively representing the capacitance values of the series resonance capacitors of the first receiving coil of the first layer, the first receiving coil of the second layer and the first receiving coil of the kth layer; r is am 、R bn And R kp Respectively representing the internal resistance values of the mth receiving coil of the first layer, the nth receiving coil of the second layer and the pth receiving coil of the kth layer; l is am 、L bn And L kp Respectively showing the m-th receiving coil of the first layer and the n-th receiving line of the second layerSelf-inductance values of the loop and the kth receiving coil of the kth layer; c am 、C bn And C kp Respectively representing the capacitance values of series resonance capacitors of the mth receiving coil of the first layer, the nth receiving coil of the second layer and the pth receiving coil of the kth layer; m 1a1 、M 1am 、M 12 And M 1k Respectively representing mutual inductance values between the first-layer transmitting coil and the first receiving coil, the first-layer mth receiving coil, the second-layer relay transmitting coil and the kth relay transmitting coil; m 2b1 、M 2bn 、M 21 And M 2k Respectively representing mutual inductance values between the second layer relay transmitting coil and a first receiving coil of the second layer, an nth receiving coil of the second layer, a transmitting coil of the first layer and a relay transmitting coil of the kth layer; m kk1 、M kkp 、M k1 And M k(k-1) Respectively represent the mutual inductance values between the kth layer relay transmitting coil and the kth layer first receiving coil, the kth layer p-th receiving coil, the first layer transmitting coil and the k-1 layer relay transmitting coil.
According to the formula (1), a current expression of each receiving coil of each layer is solved. Ensuring equal load currents in the layers, i.e. I RXa1 ＝…＝I RXam ＝I RXb1 ＝…I RXbn ＝I RXk1 ＝…＝I RXkp . And assuming that the receiving coils of the same layer are completely the same and are symmetrically and uniformly distributed around the axis of the transmitting coil, the mutual inductance value between the receiving coils and the transmitting coil or the relay transmitting coil of the same layer is approximately equal, and the current passing through any receiving coil of the same layer is equal. On the premise that all coils satisfy the resonance condition, considering only the first layer and the second layer, equation 1 can be simplified as:
Figure GDA0003759769520000061
wherein m and n respectively represent the number of the receiving coils of the first layer and the second layer,
Figure GDA0003759769520000062
and
Figure GDA0003759769520000063
respectively representing the current passing in all the receiving coils of the first layer and all the receiving coils of the second layer. Solving the expression of the current passing through the transmitting coil TX1, the current passing through the first layer of receiving coil, the current passing through the relay transmitting coil TX2 of the second layer and the current passing through the second layer of receiving coil is shown as formula (3):
Figure GDA0003759769520000071
when the sizes of the transmitting coil and the relay transmitting coil are completely consistent and the size of the receiving coil design of each layer is completely consistent, the following four conditions are met: 1) the resistance of the receiving coil loops of different layers is equal, 2) the resistance of the transmitting coil and the relay transmitting coil loops is equal, 3) the mutual inductance value of the transmitting coil or the relay transmitting coil and the receiving coil in the same layer is equal to that of other layers, 4) the number of the receiving coils in each layer is the same, namely:
Figure GDA0003759769520000072
in order to equalize the received power of all loads, i.e. the current I passed by the receiving coil of the first layer RX1 And the current I passed by the second layer winding coil RX2 Equally, the following equation can be derived:
Figure GDA0003759769520000073
it can be seen that the mutual inductance value between the first layer transmitting coil and the second layer relay transmitting coil is adjusted, so that the current I passed by the first layer receiving coil can be enabled to pass RX1 And the current I passed by the second layer winding coil RX2 And are equal.
From the flux formula in the + z-axis direction and the flux linkage formula Ψ — N Φ, it can be deduced that:
Figure GDA0003759769520000081
in the formula, Ψ 21 Representing the flux linkage, Φ, through the transmitting coil TX1 and the relay transmitting coil TX2 s1 、Φ s2 And phi sn Respectively representing the magnetic fluxes of the 1 st, 2 nd and n-th turns of the coil in the relay transmitter coil, M 12 And M 21 Representing the mutual inductance between the transmitter coil and the relay transmitter coil, I TX1 Representing the current through the transmitting coil, mu 0 Denotes the vacuum permeability, n 1 And n 2 Indicating the number of turns of the transmitting coil and the repeating transmitting coil, d and d, respectively 1 Respectively representing the turn-to-turn distance of the transmitting coil and the relay transmitting coil, wherein the outer radius of the transmitting coil is R, the inner radius of the relay transmitting coil is R ', and the value range of the radius R of the relay transmitting coil is 0-R' + (j-1) d 1 H represents the distance between the relay transmitting coil and the transmitting coil, and phi represents the angle without practical meaning.
It can be seen that the mutual inductance between the transmit coil and the relay transmit coil is related to the respective number of coil turns, the inner and outer coil diameters, the coil turn spacing, and the two coil spacing. Mutual inductance M between the two coils, in the case where the design parameters of both the transmitting coil and the repeating transmitting coil are well-defined 12 The size is only related to the spacing H of the two coils.
The correspondence of the mutual inductance between the two coils with the change in distance can be derived from equation (6), as shown in fig. 4. When the coil size parameters are determined, loop resistances of the transmitting coil and the relay transmitting coil are adjusted by means of series-parallel connection resistances or impedance matching networks according to changes of the distance H between the actual transmitting coil and the second layer of relay transmitting coil, so that mutual inductance values between the two coils meeting the limited conditions are adjusted to be in accordance with the corresponding relation of the distance between the coils, and the current passing through each layer of receiving coil is guaranteed to be equal.
When the multilayer situation is considered, the same method can be adopted to determine the limiting conditions of mutual inductance values between the transmitting coil and the relay transmitting coil when the received power of all the loads is equal, so that the multi-node output power balance in the three-dimensional space is realized.
The scheme can be applied to a wireless charging system of an electric automobile in a multi-layer stereo garage, a wireless charging system of Wireless Sensor Network (WSNs) node equipment, a wireless charging system of supermarket multi-layer shelf electronic labels (ESLs) and the like, and has high practical value. Due to the fact that the supermarket electronic tag is wirelessly powered, the required power is low, the building environment is simple and easy to achieve, and the wireless power supply system of the supermarket electronic tag is simulated to verify the validity of the scheme. The electronic tag is equivalent to a load, the electronic tag is connected to each layer of receiving coil, the transmitting coil is laid under the lowest shelf, the relay transmitting coil is laid under the rest shelves, and only the transmitting coil at the lowest layer is electrified.
In specific implementation, the required R can be determined by the formulas 5 and 6 according to the distance between each layer of the common supermarket shelf T The electronic tag wireless power supply system is designed to be suitable for the electronic tag wireless power supply system when the height of the rack is fixed; the mutual inductance value between the two coils meeting the limited conditions can be adjusted to be in accordance with the corresponding relation with the distance between the coils by changing the loop resistance of the transmitting coil and the relay transmitting coil in a series-parallel connection resistance or impedance matching network mode when the distance between each layer of the automatic telescopic frame is changed. The invention can keep the currents passing through the winding coils of each layer equal without a large current at a power supply end, thereby ensuring the multi-node output power balance in a three-dimensional space.

Claims (5)

1. A three-dimensional space multi-node power balance wireless power supply system is characterized in that aiming at a wireless power supply system with a disc-type spiral structure, a transmitting coil is arranged below a receiving coil at the same height in a three-dimensional space, so that the receiving coil at the same height is symmetrically positioned around the axis of the corresponding transmitting coil; among the transmitting coils with different heights, only the transmitting coil at the bottommost layer is electrified, and the rest transmitting coils are used as relay transmitting coils and are not electrified;
a power supply method based on a three-dimensional multi-node power balance wireless power supply system comprises the following steps:
step 1, establishing a corresponding relation of mutual inductance between a transmitting coil and a relay transmitting coil along with distance change according to coil parameters;
step 2, determining the limiting conditions of mutual inductance values between the transmitting coils and the relay transmitting coils when the receiving powers of all the loads are equal;
step 3, weakening or enhancing loop resistance of the transmitting coil and the relay transmitting coil to adjust mutual inductance value between the two coils meeting the limiting condition, so that the mutual inductance value accords with the corresponding relation of the distance between the two coils, and power balance wireless power supply is realized;
for a double-layer load, in step 1, the mutual inductance and the distance between the transmitting coil and the relay transmitting coil satisfy the following relationship:
Figure FDA0003759769510000011
in the formula, Ψ 21 Representing the flux linkage through the transmitting coil TX1 and the relay transmitting coil TX2, Φ sn Representing the magnetic flux of the n-th turn of the relay transmitter coil, M 12 And M 21 Representing the mutual inductance between the transmitter coil and the relay transmitter coil, I TX1 Representing the current through the transmitting coil, mu 0 Denotes the vacuum permeability, n 1 And n 2 Indicating the number of turns of the transmitting coil and the repeating transmitting coil, d and d, respectively 1 Respectively representing the turn-to-turn distance of the transmitting coil and the relay transmitting coil, wherein the outer radius of the transmitting coil is R, the inner radius of the relay transmitting coil is R ', and the radius R of the relay transmitting coil ranges from 0 to R' + (j-1) d 1 H represents the distance between the relay transmitting coil and the transmitting coil, phi represents an angle, and has no practical significance.
2. The system according to claim 1, wherein the transmitting coil and the relay transmitting coil are the same size.
3. The system according to claim 1, wherein the number and size of the receiving coils in each layer are the same.
4. The wireless power supply system for spatial multi-node power equalization according to claim 1, wherein in step 2, neglecting the mutual influence between the receiving coils and the influence of the transmitting coils or the relay transmitting coils on the receiving coils in different layers, the KVL equation is written for the transmitting coils in the first layer, the relay transmitting coils in the second layer and the receiving coils in the second layer respectively:
Figure FDA0003759769510000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003759769510000022
representing the input voltage, omega is the angular frequency, m and n represent the number of receiving coils of the first layer and the second layer respectively,
Figure FDA0003759769510000023
and
Figure FDA0003759769510000024
respectively representing the current passing through all the receiving coils of the first layer and all the receiving coils of the second layer, R TX1 And R TX2 Respectively representing the internal resistance, R, of the first layer transmitting coil and the second layer relay transmitting coil a1 And R b1 Respectively representing the internal resistance values, M, of the first receiving coil of the first layer and the first receiving coil of the second layer 1a1 Representing the mutual inductance, M, between the transmitter coil of the first layer and the first receiver coil of the first layer 2b1 Representing the mutual inductance, M, between the second layer relay transmitter coil and the second layer first receiver coil 12 And M 21 Representing the mutual inductance between the first layer of transmitter coils and the second layer of relay transmitter coils, M 21 Representing a mutual inductance value between the second layer relay transmitter coil and the first layer transmitter coil;
solving the expressions of the current passed by the transmitting coil TX1 and the current passed by the first layer receiving coil, and the current passed by the relay transmitting coil TX2 of the second layer and the current passed by the second layer receiving coil as follows:
Figure FDA0003759769510000031
when the sizes of the transmitting coil and the relay transmitting coil are completely consistent and the size of the receiving coil design of each layer is completely consistent, the following four conditions are met: 1) the resistance of the loops of the receiving coils on different layers is equal, 2) the resistance of the loops of the transmitting coil and the relay transmitting coil is equal, 3) the mutual inductance value of the transmitting coil or the relay transmitting coil and the receiving coil on the same layer is equal to that of other layers, 4) the number of the receiving coils on each layer is the same, namely:
Figure FDA0003759769510000032
in order to equalize the received power of all loads, i.e. the current I passed by the receiving coil of the first layer RX1 And the second layer receives the current I passing through the coil RX2 The constraint to derive the mutual inductance values is as follows:
Figure FDA0003759769510000033
5. the wireless power supply system with three-dimensional space and multi-node power balance as claimed in claim 4, wherein in step 3, loop resistances of the transmitting coil and the relay transmitting coil are weakened or strengthened by means of series-parallel resistances or impedance matching networks, so as to adjust a mutual inductance value between the two coils which meets a defined condition, so that the mutual inductance value conforms to a corresponding relationship with a coil pitch.
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