CN110808640B - Method for determining power transmission efficiency of magnetic resonance type wireless electric energy transmission system - Google Patents

Method for determining power transmission efficiency of magnetic resonance type wireless electric energy transmission system Download PDF

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CN110808640B
CN110808640B CN201910904647.XA CN201910904647A CN110808640B CN 110808640 B CN110808640 B CN 110808640B CN 201910904647 A CN201910904647 A CN 201910904647A CN 110808640 B CN110808640 B CN 110808640B
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representing
observation
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CN110808640A (en
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汪金刚
赵鹏程
沈晨
李汶江
陈铁
曾湘隆
沈红莲
陈静
熊浩
唐娟
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Chongqing University
State Grid Corp of China SGCC
Maintenance Branch of State Grid Chongqing Electric Power Co Ltd
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Chongqing University
State Grid Corp of China SGCC
Maintenance Branch of State Grid Chongqing Electric Power Co Ltd
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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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Abstract

The invention provides a method for determining the power transmission efficiency of a magnetic resonance type wireless electric energy transmission system, which is based on the research of an electromagnetic field, provides a method for determining the power transmission efficiency of the magnetic resonance type wireless electric energy transmission system, proposes a power transmission model of the wireless electric energy transmission system, and calculates the transmission power of the wireless electric energy transmission system according to the model. The invention discloses the essence of system energy transmission based on a magnetic field analysis model of a system coil, thereby constructing a calculation model of the power transmission efficiency of the magnetic resonance type wireless electric energy transmission system, and the technical precision of the power transmission efficiency is high, and the operation is simple and convenient.

Description

Method for determining power transmission efficiency of magnetic resonance type wireless electric energy transmission system
Technical Field
The invention relates to the field of wireless power transmission, in particular to a method for determining the power transmission efficiency of a magnetic resonance type wireless power transmission system.
Background
Wireless Power Transmission (WPT), also called Contactless Power Transmission (CPT), is a technology for energy transfer by means of electromagnetic fields or waves, generally using inductively coupled Power Transmission technology, and the two most concerned Transmission modes in Wireless Power Transmission technology are electromagnetic induction type and electromagnetic resonance type, wherein the magnetic resonance type Wireless Power Transmission technology has the advantage of long Transmission distance and gradually becomes the main mode of the current Wireless Power Transmission technology. The power transmission efficiency is a key index for describing an inductive coupling wireless power transmission system, the conventional power transmission efficiency is based on a mutual inductance theory, the transmitted power is represented by a mutual inductance value M between two coils and a mathematical relation of a coupling system K, but the mutual inductance value M and the coupling coefficient K are parameters which are difficult to directly calculate. The technical solutions proposed at present mainly include: firstly, a system model is built through Maxwell simulation software to obtain a mutual inductance value of a coil, and then the output power and efficiency of the system are calculated based on a mutual inductance theory and a circuit theory; secondly, acquiring voltage and current parameters of the output side of the system according to the coupling coefficient k through Spice simulation software, and further calculating the output power and efficiency of the system; and thirdly, simplifying a formula according to the experience of the mutual inductance value M, and directly calculating the efficacy through a mutual inductance theory and a circuit theory. In the method, the mutual inductance value M is obtained through finite element simulation, and then the system efficacy is calculated, on one hand, the simulation time is greatly increased along with the increase of the system complexity, and on the other hand, when the system coil parameters are changed, a simulation model needs to be built again to obtain the mutual inductance value between the coils, and the workload is large; through the calculation method of Spice simulation software, although the workload of building a model for many times is avoided, the given parameter coupling coefficient k cannot be accurately obtained directly according to the system structure parameters, and other methods or ways need to be searched for obtaining; the mutual inductance value obtained through an empirical simplified formula has the problems that a calculation result and a simulation result have large errors, and the mutual inductance value is a small parameter, so that the small errors bring large deviation of an efficacy calculation result. In addition, the influence of the system structure parameters on the space magnetic field is not essentially explored by the method.
Therefore, a method for power transmission efficiency of a magnetic coupling wireless power transmission system is needed to substantially reveal the nature of the system energy transmission.
Disclosure of Invention
In view of this, the present invention provides a method for determining power transmission efficiency of a magnetic coupling wireless power transmission system, which reveals essence of system energy transmission based on a magnetic field analysis model of a system coil, so as to construct a calculation model of the power transmission efficiency of a magnetic resonance type wireless power transmission system.
The invention provides a method for determining the power transmission efficiency of a magnetic resonance type wireless electric energy transmission system, which is characterized by comprising the following steps: the method comprises the following steps:
the power transmission efficiency eta of the wireless electric energy transmission system is determined by adopting the following method:
Figure GDA0003440087330000021
where eta represents transmission efficiency, PoutRepresenting output power, PinRepresents the input power;
the output power PoutIs determined by simultaneous equations (2) and (3):
Figure GDA0003440087330000022
wherein, PoutDenotes the output power, I2Representing the effective value of the current in the receiving loop, RLRepresenting the receiver coil load, mu0Denotes the vacuum permeability, ω denotes the angular velocity, σ denotes the electrical conductivity, N denotes the number of coil turns, R denotes the coil radius, a denotes the coil wire diameter, I1mDenotes the maximum value of the primary coil current, l denotes the number of coil radius divisions, and i is a variable of 1,2, …, Nh，NhRepresenting the mean division per turn of the transmitting coilSegment number, j is variable j 1,2, …, N indicates the number of coil turns, h is variable h 1,2,3, m, m indicates the number of observation subunits, dlR _ z indicates the number of observation subunits, andTrepresenting an intermediate variable, dlR _ zT＝dlxT*RyT-dlyT*RxTWherein, dlxTRepresenting the x-component, Ry, of a differential current element on the transmitting coilTRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, dlyTRepresenting the y-component of a differential current element on the transmitting coil, RxTThe component of the differential current element pointing to the center of the small observation circle along the direction of the x axis is shown, the j-th turn in the transmitting coil and the magnetic field generated by the i-th section of the current element at the observation plane point H of the receiving coil are shown,
Figure GDA0003440087330000031
representing the distance between the midpoint of the ith section of current element in the jth turn coil of the transmitting coil and the observation plane point H of the receiving coil;
wherein the input power PinIs determined by simultaneous equations (4) and (5):
Figure GDA0003440087330000032
wherein, PinRepresenting input power, U1Representing the effective value of the voltage of the transmission loop, I1Representing the effective value of the current of the transmission loop, mu0Denotes the vacuum permeability, ω denotes the angular velocity, σ denotes the electrical conductivity, N denotes the number of coil turns, R denotes the coil radius, a denotes the coil wire diameter, I2mThe maximum value of the current of the receiving loop is shown, l represents the number of coil radius dividing sections, and i is a variable i is 1,2, …, Nh，NhThe average division number of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, g is a variable g which is 1,2,3, m, m is the number of observation subunits, dlR-zRRepresenting intermediate variables, dlR-zR＝dlxR*RyR-dlyR*RxR，dlxRRepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-axis component of the differential current element on the receiving coil,RyRrepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, RxRRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000033
the distance between the middle point of the ith segment of current element in the jth turn coil of the receiving coil and the observation plane point G of the receiving coil is shown.
Further, the receiving of the return current I2Determined by simultaneous equations (6) to (11),
Figure GDA0003440087330000034
wherein, I2Representing the effective value of the current of the receiving loop, I2mRepresenting the maximum value of the current of the receiving loop circuit;
Figure GDA0003440087330000035
wherein, I2mIndicating the maximum value of the current in the receiving loop, i2Representing the receive loop current transient, ω representing angular velocity,
Figure GDA0003440087330000041
represents a phase angle;
Figure GDA0003440087330000042
wherein i2Representing instantaneous value of current, u, of receiving loop2Representing instantaneous value of the voltage of the receiving loop, RΩThe resistance of the ohmic losses is expressed in terms of,
Figure GDA0003440087330000043
wherein, mu0Denotes the vacuum permeability, ω denotes the angular velocity, σ denotes the electrical conductivity, a denotes the coil wire diameter, N denotes the number of coil turns, R denotes the coil radius, R denotes the coil wire diameterLRepresenting the receive loop load;
Figure GDA0003440087330000044
wherein u is2Representing instantaneous value of the voltage of the receiving loop, N2Indicating the number of receiver coil turns, where N2＝N，φ21Represents the current i1A generated magnetic flux passing perpendicularly through the receiving coil;
φ21≈φTR (10)
wherein phi is21Represents the current i1The generated magnetic flux, phi, passing perpendicularly through the receiving coilTRRepresenting the receiver coil viewing plane magnetic flux;
Figure GDA0003440087330000045
wherein phi isTRDenotes the flux of the receiver coil in the observation plane, N denotes the number of turns of the coil, dlR-ZTExpressed as an intermediate variable, R represents the coil radius, l represents the number of coil radius divisions, and i is a variable i-1, 2, …, Nh，NhThe number of the evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, h is a variable h which is 1,2,3, wherein m is the number of observation subunits, dlR _ z is representedTRepresenting an intermediate variable, dlR _ zT＝dlxT*RyT-dlyT*RxTWherein, dlxTRepresenting the x-component, Ry, of a differential current element on the transmitting coilTRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, dlyTRepresenting the y-component of a differential current element on the transmitting coil, RxTRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000046
the distance between the middle point of the ith section of current element in the jth turn coil of the transmitting coil and the observation plane point H of the receiving coil is shown.
Further, the receiving coil observes a planar flux phiTRObtained by the following method:
s1: establishing a cylindrical spiral resonance coil analysis model under a three-dimensional rectangular coordinate system; the central axis of the transmitting coil and the central axis of the receiving coil are coincided with the Z axis, wherein the center of the circle of the bottom surface of the transmitting coil is coincided with the far point of the coordinate axis, and the receiving coil is positioned above the transmitting coil and is positioned at the position D;
s2: dividing each turn of transmitting coil into NhA segment;
s3: determining an observation plane; the cross section of the coil in the middle is an observation plane;
s4: drawing an observation subunit on the observation plane;
s5: calculating the magnetic flux phi generated by the transmitting coil in the observation subunitTRh；
Figure GDA0003440087330000051
Wherein phi isTRhThe magnetic flux generated by the transmitting coil in the observation subunit is shown, R represents the coil radius, l represents the number of coil radius division segments, and i is the variable i is 1,2, …, Nh，NhThe number of the evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, h is a variable h which is 1,2,3, wherein m is the number of observation subunits, dlR _ z is representedTRepresenting an intermediate variable, dlR _ zT＝dlxT*RyT-dlyT*RxTWherein, dlxTRepresenting the x-component, Ry, of a differential current element on the transmitting coilTRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, dlyTRepresenting the y-component of a differential current element on the transmitting coil, RxTRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000053
representing the distance between the midpoint of the ith section of current element in the jth turn coil of the transmitting coil and the observation plane point H of the receiving coil;
s6: the magnetic flux generated by the transmitter coil in the observation plane is calculated.
Further, the step S4 of drawing the observation sub-unit on the observation plane includes the steps of:
s41: equally dividing the radius of the coil into l sections;
s42: using the center of a circle of the observation plane as the center of a circle
Figure GDA0003440087330000052
Drawing concentric circles for the radius, wherein R denotes the coil radius, l denotes the number of coil radius divisions, and k denotes a variable, wherein k is 1,3,5 … (l-1);
s43: the center of the observation subunit is positioned on the circumference of the concentric circle, so as to
Figure GDA0003440087330000061
Drawing observation subunits, wherein every two observation subunits are tangent, wherein R represents the radius of the coil, and l represents the number of coil radius division sections;
s44: step S43 is repeated until the observation plane cannot draw an observation subunit satisfying step S43.
Further, the effective value U1 of the transmit loop voltage is obtained by the following method:
U1＝U11+U12 (13)
wherein, U1Representing the effective value of the voltage of the transmission loop, U11Indicating the value of the voltage, U, generated by the transmitting coil itself12Representing the induced voltage of the receiving coil to the transmitting coil,
U11＝I1RΩ (14)
wherein, U11Representing the value of the voltage generated by the transmitting coil itself, I1Representing the effective value of the current of the transmitting loop, RΩThe resistance of the ohmic losses is expressed in terms of,
Figure GDA0003440087330000062
wherein, mu0Denotes the magnetic permeability in vacuum, ω denotes the angular velocity, and σ denotes the electricityConductivity, N represents the number of coil turns, R represents the coil radius,
Figure GDA0003440087330000063
wherein, U12Indicating the induced voltage of the receiving coil to the transmitting coil, U12mRepresents the maximum value of the induced voltage of the receiving coil to the transmitting coil,
Figure GDA0003440087330000064
wherein, U12mRepresenting the maximum value of the induced voltage, U, of the receiving coil to the transmitting coil12Representing the induced voltage of the receiver coil to the transmitter coil, omega representing the angular velocity,
Figure GDA0003440087330000065
represents a phase angle;
Figure GDA0003440087330000071
wherein, U12Representing the induced voltage of the receiving coil to the transmitting coil, N1Indicating the number of transmitter coil turns, where N1＝N2＝N，φ12Representing the magnetic flux generated by the receiver coil at the transmitter coil;
φ12≈φRT
(18)
wherein phi is12Representing the magnetic flux generated by the receiver coil at the transmitter coil; phi is aRTRepresenting the transmitter coil observation plane magnetic flux;
Figure GDA0003440087330000072
wherein phi isRTRepresenting the flux in the observation plane of the transmitter coil, R representing the coil radius, l representing the division of the coil radiusThe number of stages, i being the variable i ═ 1,2, …, Nh，NhThe number of the evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, g is a variable g which is 1,2,3, m and m are the number of observation subunits, dlR _ z is representedRRepresenting an intermediate variable, dlR _ zR＝dlxR*RyR-dlyR*RxR，dlxRRepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-component, Ry, of a differential current element on the receiving coilRRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, RxRRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000073
the distance between the middle point of the ith segment of current element in the jth turn coil of the receiving coil and the observation plane point G of the receiving coil is shown.
Further, the transmitting coil observes a planar magnetic flux phiRTObtained by the following method:
s1: establishing a cylindrical spiral resonance coil analysis model under a three-dimensional rectangular coordinate system; the central axis of the transmitting coil and the central axis of the receiving coil are coincided with the Z axis, wherein the center of the circle of the bottom surface of the transmitting coil is coincided with the far point of the coordinate axis, and the receiving coil is positioned above the transmitting coil and is positioned at the position D;
s2: dividing each turn of receiving coil into NhA segment;
s3: determining an observation plane; the cross section of the middle part of the transmitting coil is an observation plane;
s4: drawing an observation subunit on the observation plane;
s5: calculating the magnetic flux generated by the transmitting coil in the observation subunit
Figure GDA0003440087330000081
Figure GDA0003440087330000082
Wherein the content of the first and second substances,
Figure GDA0003440087330000083
the magnetic flux generated by the receiving coil in the observation subunit is shown, R represents the coil radius, l represents the number of coil radius division segments, and i is a variable i is 1,2, …, Nh，NhThe number of the evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, g is a variable g which is 1,2,3, m and m are the number of observation subunits, dlR _ z is representedRRepresenting an intermediate variable, dlR _ zR＝dlxR*RyR-dlyR*RxR，dlxRRepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-component, Ry, of a differential current element on the receiving coilRRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, RxRRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000084
representing the distance between the midpoint of the ith section of current element in the jth turn coil of the receiving coil and the observation plane point G of the receiving coil;
s6: the magnetic flux generated by the transmitter coil in the observation plane is calculated.
Further, the step S4 of drawing the observation sub-unit on the observation plane includes the steps of:
s41: equally dividing the radius of the coil into l sections;
s42: using the center of a circle of the observation plane as the center of a circle
Figure GDA0003440087330000085
Drawing concentric circles for the radius, wherein R denotes the coil radius, l denotes the number of coil radius divisions, and k denotes a variable, wherein k is 1,3,5 … (l-1);
s43: the center of the observation subunit is positioned on the circumference of the concentric circle, so as to
Figure GDA0003440087330000086
The observation subunit is drawn as a radius, andthe two observation subunits are tangent, wherein R represents the radius of the coil, and l represents the number of coil radius division sections;
s44: step S43 is repeated until the observation plane cannot draw an observation subunit satisfying step S43.
The invention has the beneficial technical effects that: the invention discloses the essence of system energy transmission based on a magnetic field analysis model of a system coil, thereby constructing a calculation model of the power transmission efficiency of the magnetic resonance type wireless electric energy transmission system, and the technical precision of the power transmission efficiency is high, and the operation is simple and convenient.
Drawings
The invention is further described below with reference to the following figures and examples:
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a space magnetic field analysis model of the cylindrical spiral resonance coil of the present invention.
FIG. 3 is a schematic view of the division of the observation plane according to the present invention.
Detailed Description
The invention is further described with reference to the accompanying drawings in which:
the invention provides a method for determining the power transmission efficiency of a magnetic resonance type wireless electric energy transmission system, which is characterized by comprising the following steps: the method comprises the following steps:
the power transmission efficiency eta of the wireless electric energy transmission system is determined by adopting the following method:
Figure GDA0003440087330000091
where eta represents transmission efficiency, PoutRepresenting output power, PinRepresents the input power;
the output power PoutIs determined by simultaneous equations (2) and (3):
Figure GDA0003440087330000092
wherein, PoutDenotes the output power, I2Representing the effective value of the current in the receiving loop, RLRepresenting the receiver coil load, mu0Denotes the vacuum permeability, ω denotes the angular velocity, σ denotes the electrical conductivity, N denotes the number of coil turns, R denotes the coil radius, a denotes the coil wire diameter, I1mDenotes the maximum value of the primary coil current, l denotes the number of coil radius divisions, and i is a variable of 1,2, …, Nh，NhThe number of the evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, h is a variable h which is 1,2,3, wherein m is the number of observation subunits, dlR _ z is representedTRepresenting an intermediate variable, dlR _ zT＝dlxT*RyT-dlyT*RxTWherein, dlxTRepresenting the x-component, Ry, of a differential current element on the transmitting coilTRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, dlyTRepresenting the y-component of a differential current element on the transmitting coil, RxTThe component of the differential current element pointing to the center of the small observation circle along the direction of the x axis is shown, the j-th turn in the transmitting coil and the magnetic field generated by the i-th section of the current element at the observation plane point H of the receiving coil are shown,
Figure GDA0003440087330000101
representing the distance between the midpoint of the ith section of current element in the jth turn coil of the transmitting coil and the observation plane point H of the receiving coil;
wherein the input power PinIs determined by simultaneous equations (4) and (5):
Figure GDA0003440087330000102
wherein, PinRepresenting input power, U1Representing the effective value of the voltage of the transmission loop, I1Representing the effective value of the current of the transmission loop, mu0Denotes the vacuum permeability, ω denotes the angular velocity, σ denotes the electrical conductivity, N denotes the number of coil turns, R denotes the coil radius, a denotes the coil wire diameter, I2mThe maximum value of the current of the receiving loop is shown, l represents the number of coil radius dividing sections, and i is a variable i is 1,2, …, Nh，NhIndicating a transmitting coilThe number of equally divided segments per turn, j being the variable j being 1,2, …, N representing the number of coil turns, g being the variable g being 1,2,3RRepresenting an intermediate variable, dlR _ zR＝dlxR*RyR-dlyR*RxR，dlxRRepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-component, Ry, of a differential current element on the receiving coilRRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, RxRRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000103
the distance between the middle point of the ith segment of current element in the jth turn coil of the receiving coil and the observation plane point G of the receiving coil is shown.
By the technical scheme, a calculation model of the power transmission efficiency of the magnetic resonance type wireless electric energy transmission system is constructed, the technical precision of the power transmission efficiency is high, and the operation is simple and convenient.
In this embodiment, the receiving the return current I2Determined by simultaneous equations (6) to (11),
Figure GDA0003440087330000104
wherein, I2Representing the effective value of the current of the receiving loop, I2mRepresenting the maximum value of the current of the receiving loop circuit;
Figure GDA0003440087330000105
wherein, I2mIndicating the maximum value of the current in the receiving loop, i2Representing the receive loop current transient, ω representing angular velocity,
Figure GDA0003440087330000106
represents a phase angle;
Figure GDA0003440087330000111
wherein i2Representing instantaneous value of current, u, of receiving loop2Representing instantaneous value of the voltage of the receiving loop, RΩThe resistance of the ohmic losses is expressed in terms of,
Figure GDA0003440087330000112
wherein, mu0Denotes the vacuum permeability, ω denotes the angular velocity, σ denotes the electrical conductivity, N denotes the number of coil turns, R denotes the coil radius, R denotes the number of coil turnsLRepresenting the receive loop load;
Figure GDA0003440087330000113
wherein u is2Representing instantaneous value of the voltage of the receiving loop, N2Indicating the number of receiver coil turns, where N2＝N，φ21Represents the current i1A generated magnetic flux passing perpendicularly through the receiving coil;
φ21≈φTR (10)
wherein phi is21Represents the current i1The generated magnetic flux, phi, passing perpendicularly through the receiving coilTRRepresenting the receiver coil viewing plane magnetic flux;
Figure GDA0003440087330000114
wherein phi isTRDenotes the flux of the receiver coil in the observation plane, N denotes the number of turns of the coil, dlR-ZTExpressed as an intermediate variable, R represents the coil radius, l represents the number of coil radius divisions, and i is a variable i-1, 2, …, Nh，NhThe number of the evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, h is a variable h which is 1,2,3, wherein m is the number of observation subunits, dlR _ z is representedTRepresenting an intermediate variable, dlR _ zT＝dlxT*RyT-dlyT*RxTWherein, dlxTRepresenting the x-component, Ry, of a differential current element on the transmitting coilTRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, dlyTRepresenting the y-component of a differential current element on the transmitting coil, RxTRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000115
the distance between the middle point of the ith section of current element in the jth turn coil of the transmitting coil and the observation plane point H of the receiving coil is shown.
In this embodiment, the receiving coil observes a planar flux phiTRObtained by the following method:
s1: establishing a cylindrical spiral resonance coil analysis model under a three-dimensional rectangular coordinate system; the central axis of the transmitting coil and the central axis of the receiving coil are coincided with the Z axis, wherein the center of the circle of the bottom surface of the transmitting coil is coincided with the far point of the coordinate axis, and the receiving coil is positioned above the transmitting coil and is positioned at the position D;
s2: dividing each turn of transmitting coil into NhA segment;
s3: determining an observation plane; the cross section of the coil in the middle is an observation plane;
s4: drawing an observation subunit on the observation plane, wherein the observation subunit is a small observation circle;
s5: calculating the magnetic flux generated by the transmitting coil in the observation subunit
Figure GDA0003440087330000121
Figure GDA0003440087330000122
Wherein the content of the first and second substances,
Figure GDA0003440087330000123
the magnetic flux generated by the transmitting coil in the observation subunit is shown, R represents the coil radius, l represents the number of coil radius division segments, and i is the variable i is 1,2, …, Nh，NhThe number of evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, h is a variable h which is 1,2,3, wherein m is the number of observation subunits, dlR-z is the number of observation subunits, andTrepresenting intermediate variables, dlR-zT＝dlxT*RyT-dlyT*RxTWherein, dlxTRepresenting the x-component, Ry, of a differential current element on the transmitting coilTRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, dlyTRepresenting the y-component of a differential current element on the transmitting coil, RxTRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000124
representing the distance between the midpoint of the ith section of current element in the jth turn coil of the transmitting coil and the observation plane point H of the receiving coil;
s6: the magnetic flux generated by the transmitter coil in the observation plane is calculated.
In this embodiment, the step S4 of drawing the observation subunit on the observation plane includes the following steps:
s41: equally dividing the radius of the coil into l sections;
s42: using the center of a circle of the observation plane as the center of a circle
Figure GDA0003440087330000125
Drawing concentric circles for the radius, wherein R denotes the coil radius, l denotes the number of coil radius divisions, and k denotes a variable, wherein k is 1,3,5 … (l-1);
s43: the center of the observation subunit is positioned on the circumference of the concentric circle, so as to
Figure GDA0003440087330000126
Drawing observation subunits, wherein every two observation subunits are tangent, R represents the radius of the coil, l represents the number of coil radius division sections, and the observation subunits are small observation circles;
s44: step S43 is repeated until the observation plane cannot draw an observation subunit satisfying step S43, which is a small observation circle, as shown in fig. 3.
Let the circle center coordinate of each small circle h be (x)h,yh,zh) Analysis of the current i flowing through the transmitting coil1，
Figure GDA0003440087330000131
The magnetic induction intensity at the center of the h-th small observation circle of the receiving coil
Figure GDA0003440087330000132
The size of (2).
Firstly, the average of each turn is calculated to be NhIn the transmitting coils of the segments, the corresponding coordinates of the starting point and the end point of the current element of the ith segment in the jth turn coil are respectively shown as formulas (21) and (22).
Figure GDA0003440087330000133
Wherein the content of the first and second substances,
Figure GDA0003440087330000134
the current element of the ith segment in the jth turn coil in the transmitting coil is correspondingly positioned at the coordinate of the starting point of the X axis,
Figure GDA0003440087330000135
the terminal coordinate of the ith section of current element in the jth turn coil in the transmitting coil correspondingly positioned on the X axis is shown,
Figure GDA0003440087330000136
the current element of the ith segment in the jth turn coil in the transmitting coil is correspondingly positioned at the coordinate of the starting point of the y axis,
Figure GDA0003440087330000137
the terminal coordinate of the ith section of current element in the jth turn coil in the transmitting coil corresponding to the y axis is shown,
Figure GDA0003440087330000138
indicating that the current element of the ith segment in the jth turn coil in the transmitting coil is correspondingly positionedThe coordinates of the starting point of the Z-axis,
Figure GDA0003440087330000141
representing the terminal point coordinate of the ith section of current element in the jth turn coil in the transmitting coil correspondingly positioned on the Z axis, R represents the radius of the coil, NhThe average number of divided sections per turn of the transmitting coil is shown, a represents the wire diameter of the coil, and i is the variable i is 1,2, …, NhJ is the variable j ═ 1,2, …, N.
The distance between the middle point of the ith segment of current element in the jth turn coil and the observation plane point H of the receiving coil
Figure GDA0003440087330000142
Comprises the following steps:
Figure GDA0003440087330000143
wherein R represents the coil radius, XhThe coordinate of the circle center of the h small circle of the coil receiving coil is positioned on the X axis,
Figure GDA0003440087330000144
the current element of the ith segment in the jth turn coil of the transmitting coil is correspondingly positioned at the starting point coordinate of the X axis,
Figure GDA0003440087330000145
the terminal coordinate, y, of the ith section of current element in the jth turn coil of the transmitting coil correspondingly positioned on the X axishA coordinate indicating that the center of the h-th small circle of the receiving coil is located on the y-axis,
Figure GDA0003440087330000146
the ith section of current element in the jth turn coil of the transmitting coil is correspondingly positioned at the coordinate of the starting point of the y axis,
Figure GDA0003440087330000147
the terminal point coordinate, Z, of the ith section of current element in the jth turn coil of the transmitting coil correspondingly positioned on the y axishA coordinate indicating that the center of the h-th small circle of the receiver coil is located on the z-axis,
Figure GDA0003440087330000148
the current element of the ith segment in the jth turn coil of the transmitting coil is correspondingly positioned at the starting point coordinate of the Z axis,
Figure GDA0003440087330000149
the terminal point coordinate indicating that the ith section of current element in the jth turn coil of the transmitting coil is correspondingly positioned on the Z axis;
the magnetic field generated by the j-th turn and the i-th section of current element in the transmitting coil at the observation plane point H of the receiving coil is determined by simultaneous equations (24) to (28),
Figure GDA00034400873300001410
wherein, dlxTRepresenting the x-axis component, dly, of the differential current element on the transmitting coilTRepresenting the y-axis component of the differentiated current element on the transmit coil,
Figure GDA00034400873300001411
the current element of the ith segment in the j turn coil is correspondingly positioned at the starting point coordinate of the X axis,
Figure GDA00034400873300001412
the current element of the ith section in the j turn coil is correspondingly positioned at the terminal point coordinate of the X axis,
Figure GDA00034400873300001413
the current element of the ith segment in the j turn coil is correspondingly positioned at the coordinate of the starting point of the y axis,
Figure GDA00034400873300001414
the terminal point coordinate of the ith section of current element in the jth turn coil correspondingly positioned on the y axis is represented;
dlR_zT＝dlxT*RyT-dlyT*RxT (25)
wherein, dlR _ zTDenotes an intermediate variable, dlxTRepresenting the x-component, Ry, of a differential current element on the transmitting coilTRepresenting the differentialComponent of current element pointing to center of small observation circle along y-axis direction, dlyTRepresenting the y-component of a differential current element on the transmitting coil, RxTRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000151
wherein the content of the first and second substances,
Figure GDA0003440087330000152
represents the magnetic field, mu, generated by the j turn and i section current elements of the transmitting coil at the observation plane point H of the receiving coil0Denotes the magnetic permeability in vacuum, i1Representing transmit loop current transient, dlR _ zTRepresenting an intermediate variable, dlR _ zT＝dlxT*RyT-dlyT*RxTWherein, dlxTRepresenting the x-component, Ry, of a differential current element on the transmitting coilTRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, dlyTRepresenting the y-component of a differential current element on the transmitting coil, RxTRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000153
the distance between the middle point of the ith segment of current element in the jth turn coil and the observation plane point H of the receiving coil,
and analyzing the magnetic induction intensity generated by the transmitting coil at a certain point of the plane of the receiving coil at a certain time t. At any moment, each point B on the observation plane of the receiving coilZWhen l is large enough, the magnetic induction intensity in any small circle of the observation plane of the receiving coil can be used as a uniform magnetic field for analysis, i.e. the magnetic induction intensity of each point can be approximately equal to the magnetic induction intensity at the center h of the circle
Figure GDA0003440087330000154
The magnetic field in the z-axis direction generated at point H by the j-th turn transmit coil and the N-th turn transmit coil can be calculated.
Figure GDA0003440087330000155
Wherein the content of the first and second substances,
Figure GDA0003440087330000156
represents the magnetic field, mu, generated by the j-th turn and the i-th section of current element in the transmitting coil at the observation plane point H of the receiving coil along the Z-axis direction0Denotes the magnetic permeability in vacuum, i1Representing transmit loop current transient, dlR _ zTRepresenting an intermediate variable, dlR _ zT＝dlxT*RyT-dlyT*RxTWherein, dlxTRepresenting the x-component, Ry, of a differential current element on the transmitting coilTRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, dlyTRepresenting the y-component of a differential current element on the transmitting coil, RxTThe component of the differential current element pointing to the center of the small observation circle along the direction of the x axis is shown, i is a variable i is 1,2, …, Nh，
Figure GDA0003440087330000157
The distance between the middle point of the ith segment of current element in the jth turn coil and the observation plane point H of the receiving coil,
Figure GDA0003440087330000158
wherein, BZhI is the variable i-1, 2, …, NhJ is variable j ═ 1,2, …, N, μ0Denotes the magnetic permeability in vacuum, i1Representing transmit loop current transient, dlR _ zTRepresenting an intermediate variable, dlR _ zT＝dlxT*RyT-dlyT*RxTWherein, dlxTRepresenting the x-component, Ry, of a differential current element on the transmitting coilTRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, dlyTRepresenting the y-component of a differential current element on the transmitting coil, RxTIndicating differential current element pointing to the centre of the small observation circle along the direction of the x-axisThe components of the first and second images are,
Figure GDA0003440087330000161
the distance between the middle point of the ith section of current element in the jth turn of coil and the observation plane point H of the receiving coil;
calculating the magnetic flux of the transmitting coil on the small circle of the observation plane, and obtaining the magnetic flux in the z-axis direction in the small circle of the observation plane according to a uniform magnetic field magnetic flux calculation formula phi (BS)
Figure GDA0003440087330000162
Figure GDA0003440087330000163
Wherein the content of the first and second substances,
Figure GDA0003440087330000164
the magnetic flux in the direction of the z-axis in a small circle of the plane is observed,
Figure GDA0003440087330000165
the magnetic induction intensity of the N turns of coils generated at the point H along the Z-axis direction is represented, R represents the radius of the coils, and l represents the number of coil radius division sections; thereby calculating the magnetic flux phi generated by the transmitting coil in the whole observation plane of the receiving coilTR，
Figure GDA0003440087330000166
Wherein, phi TR represents the magnetic flux generated by the transmitting coil on the whole observation plane of the receiving coil, h is a variable h which is 1,2,3, m, m represents the number of observation subunits,
Figure GDA0003440087330000167
observing the magnetic flux in the direction of the z axis in a small circle of the plane;
in this embodiment, the effective value U1 of the transmit loop voltage is obtained by:
U1＝U11+U12 (13)
wherein, U1Representing the effective value of the voltage of the transmission loop, U11Indicating the value of the voltage, U, generated by the transmitting coil itself12Representing the induced voltage of the receiving coil to the transmitting coil,
U11＝I1RΩ (14)
wherein, U11Representing the value of the voltage generated by the transmitting coil itself, I1Representing the effective value of the current of the transmitting loop, RΩThe resistance of the ohmic losses is expressed in terms of,
Figure GDA0003440087330000168
wherein, mu0Denotes the vacuum permeability, ω denotes the angular velocity, σ denotes the electrical conductivity, N denotes the number of coil turns, R denotes the coil radius,
Figure GDA0003440087330000171
wherein, U12Indicating the induced voltage of the receiving coil to the transmitting coil, U12mRepresents the maximum value of the induced voltage of the receiving coil to the transmitting coil,
Figure GDA0003440087330000172
wherein, U12mRepresenting the maximum value of the induced voltage, U, of the receiving coil to the transmitting coil12Representing the induced voltage of the receiver coil to the transmitter coil, omega representing the angular velocity,
Figure GDA0003440087330000173
represents a phase angle;
Figure GDA0003440087330000174
wherein, U12Representing the induced voltage of the receiving coil to the transmitting coil, N1Indicating the number of transmitter coil turns, where N1＝N2＝N，φ12Representing the magnetic flux generated by the receiver coil at the transmitter coil;
φ12≈φRT
(18)
wherein phi is12Representing the magnetic flux generated by the receiver coil at the transmitter coil; phi is aRTRepresenting the transmitter coil observation plane magnetic flux;
Figure GDA0003440087330000175
wherein phi isRTDenotes the magnetic flux of the observation plane of the transmitting coil, R denotes the coil radius, l denotes the number of coil radius divisions, and i is a variable of 1,2, …, Nh，NhThe number of the evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, g is a variable g which is 1,2,3, m and m are the number of observation subunits, dlR _ z is representedRRepresenting an intermediate variable, dlR _ zR＝dlxR*RyR-dlyR*RxR，dlxRRepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-component, Ry, of a differential current element on the receiving coilRRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, RxRRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000181
the distance between the middle point of the ith segment of current element in the jth turn coil of the receiving coil and the observation plane point G of the receiving coil is shown.
In this embodiment, the transmitter coil observes a planar flux phiRTObtained by the following method:
s1: establishing a cylindrical spiral resonance coil analysis model under a three-dimensional rectangular coordinate system; the central axis of the transmitting coil and the central axis of the receiving coil are coincided with the Z axis, wherein the center of the circle of the bottom surface of the transmitting coil is coincided with the far point of the coordinate axis, and the receiving coil is positioned above the transmitting coil and is positioned at the position D; under the condition of certain current of the transmitting coil, the magnetic field generated by the observation plane of the receiving coil and the voltage and the current of the receiving loop are analyzed by adopting segmented transmission.
S2: dividing each turn of receiving coil into NhA segment;
s3: determining an observation plane; the cross section of the middle part of the transmitting coil is an observation plane; according to the Maxwell simulation result, the error between the induced voltage generated by the magnetic field change of the middle section of the receiving coil and the induced voltage generated by simulating the magnetic field of the space where the whole coil is located is not large and is basically controlled to be within 5 percent, so that the middle section of the receiving coil is selected as an observation plane as shown by a circular plane where a dotted line is located in FIG. 2;
s4: drawing an observation subunit on the observation plane, wherein the observation subunit is a small observation circle;
s5: calculating the magnetic flux generated by the transmitting coil in the observation subunit
Figure GDA0003440087330000182
Figure GDA0003440087330000183
Wherein the content of the first and second substances,
Figure GDA0003440087330000184
the magnetic flux generated by the receiving coil in the observation subunit is shown, R represents the coil radius, l represents the number of coil radius division segments, and i is a variable i is 1,2, …, Nh，NhThe average division number of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, g is a variable g which is 1,2,3, m, m is the number of observation subunits, dlR-zRIt is shown that,
Figure GDA0003440087330000185
representing the distance between the midpoint of the ith section of current element in the jth turn coil of the receiving coil and the observation plane point G of the receiving coil;
s6: the magnetic flux generated by the transmitter coil in the observation plane is calculated.
In this embodiment, the step S4 of drawing the observation subunit on the observation plane includes the following steps:
s41: equally dividing the radius of the coil into l sections;
s42: using the center of a circle of the observation plane as the center of a circle
Figure GDA0003440087330000186
Drawing concentric circles for the radius, wherein R denotes the coil radius, l denotes the number of coil radius divisions, and k denotes a variable, wherein k is 1,3,5 … (l-1);
s43: the center of the observation subunit is positioned on the circumference of the concentric circle, so as to
Figure GDA0003440087330000191
Drawing observation subunits, wherein every two observation subunits are tangent, R represents the radius of the coil, l represents the number of coil radius division sections, and the observation subunits are small observation circles;
s44: step S43 is repeated until the observation plane cannot draw an observation subunit satisfying step S43.
And calculating the space magnetic field of the resonance coil, and establishing the relation between the space magnetic field of the transmitting coil and the receiving coil and the coil parameters. According to Faraday's law of electromagnetic induction: the induced electromotive force generated by the receiving coil (transmitting coil) by the transmitting coil (receiving coil) is the magnetic field change of the space region where the receiving coil (transmitting coil) is located, and in order to simplify the magnetic field analysis process, an observation plane of the receiving coil (transmitting coil) can be set, and the magnetic field of the plane can be calculated. Because the space magnetic field of the resonance system is a time-varying magnetic field, the observation plane can be divided into a plurality of small observation circles by calculating the magnetic field of the observation plane, when the observation circle is small enough, the magnetic field at any moment in the small observation circle is approximately treated as a uniform magnetic field, then each turn of the transmitting coil (receiving coil) is segmented, the magnetic field generated by each small current section at the center of each small observation circle of the observation plane of the receiving coil (transmitting coil) is calculated and accumulated to obtain the magnetic field at the center of the small observation circle, and the total magnetic flux of the observation plane of the receiving coil (transmitting coil) can be obtained by calculating the magnetic flux of the small observation circle and accumulating, thereby realizing the calculation of the induced voltage.
Dividing the current section of the receiving coil, establishing a rectangular coordinate system as shown in fig. 3 by taking the plane of the transmitting coil as an observation plane, equally dividing the observation plane, dividing the observation plane into l sections along the radius, drawing to obtain m non-intersecting circles, and setting the center coordinate of the g-th small circle in the observation plane as (x)g，yg，zg)。
First, the receiving coil is divided equally into N turnshSegment, the coordinates of the starting point and the ending point corresponding to the current element of the ith segment in the jth turn of coil are respectively as follows:
Figure GDA0003440087330000201
Figure GDA0003440087330000202
wherein the content of the first and second substances,
Figure GDA0003440087330000203
the current element of the ith segment in the jth turn coil in the receiving coil is correspondingly positioned at the coordinate of the starting point of the X axis,
Figure GDA0003440087330000204
the terminal coordinate of the ith section of current element in the jth turn coil in the receiving coil correspondingly positioned on the X axis is shown,
Figure GDA0003440087330000205
the current element of the ith segment in the jth turn coil in the receiving coil is correspondingly positioned at the coordinate of the starting point of the y axis,
Figure GDA0003440087330000206
the terminal coordinate of the current element of the ith segment in the jth turn coil in the receiving coil corresponding to the y axis is shown,
Figure GDA0003440087330000207
indicating the corresponding position of the ith segment of current element in the jth turn coil in the receiving coilThe coordinates of the starting point on the Z-axis,
Figure GDA0003440087330000208
representing the terminal point coordinate of the ith section of current element in the jth turn coil in the receiving coil correspondingly positioned on the Z axis, R represents the radius of the coil, NhThe average number of divided sections per turn of the transmitting coil is shown, a represents the wire diameter of the coil, and i is the variable i is 1,2, …, Nh，NhThe average number of sections divided by each turn of the transmitting coil is shown, j is variable j is 1,2, …, N is the number of turns of the coil,
the distance between the middle point of the current element of the ith segment in the jth turn coil and the observation plane point G of the transmitting coil
Figure GDA0003440087330000209
Comprises the following steps:
Figure GDA0003440087330000211
wherein the content of the first and second substances,
Figure GDA0003440087330000212
the distance, x, between the midpoint of the ith segment of current element in the jth turn of coil and the observation plane point H of the receiving coilgCoordinate, y, representing the centre of the g-th small circle of the receiving coil on the X-axisgZ is a coordinate representing the center of the g-th small circle of the receiving coil on the y-axisgA coordinate indicating that the center of the g-th small circle of the receiver coil is located on the z-axis,
Figure GDA0003440087330000213
the current element of the ith segment in the jth turn coil in the receiving coil is correspondingly positioned at the coordinate of the starting point of the X axis,
Figure GDA0003440087330000214
the terminal coordinate of the ith section of current element in the jth turn coil in the receiving coil correspondingly positioned on the X axis is shown,
Figure GDA0003440087330000215
represents the ith segment of current element pair in the jth turn coil in the receiving coilShould be located at the starting point coordinate of the y-axis,
Figure GDA0003440087330000216
the terminal coordinate of the current element of the ith segment in the jth turn coil in the receiving coil corresponding to the y axis is shown,
Figure GDA0003440087330000217
the current element of the ith segment in the jth turn coil in the receiving coil is correspondingly positioned at the starting point coordinate of the Z axis,
Figure GDA0003440087330000218
the terminal coordinate of the ith section of current element in the jth turn coil in the receiving coil corresponding to the Z axis is shown,
the magnetic field generated by the j-th turn and the i-th section of current element in the receiving coil at the observation plane point G of the transmitting coil can be expressed by the simultaneous equations (33) to (37) as follows:
Figure GDA0003440087330000219
wherein, dlxRRepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-axis component of the differential current element on the receiving coil,
Figure GDA00034400873300002110
the current element of the ith segment in the jth turn coil in the receiving coil is correspondingly positioned at the coordinate of the starting point of the X axis,
Figure GDA00034400873300002111
the terminal coordinate of the ith section of current element in the jth turn coil in the receiving coil correspondingly positioned on the X axis is shown,
Figure GDA00034400873300002112
the current element of the ith segment in the jth turn coil in the receiving coil is correspondingly positioned at the coordinate of the starting point of the y axis,
Figure GDA00034400873300002113
indicating the second in the receiving coilThe ith segment of current element in the j turns of coil is correspondingly positioned at the terminal point coordinate of the y axis,
dlR_zR＝dlxR*RyR-dlyR*RxR (34)
wherein, dlR _ zRDenotes an intermediate variable, dlxRRepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-component, Ry, of a differential current element on the receiving coilRRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, RxRRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000221
wherein the content of the first and second substances,
Figure GDA0003440087330000222
represents the magnetic field, mu, generated by the j turn and i section current elements of the receiving coil at the observation plane point H of the transmitting coil0Denotes the magnetic permeability in vacuum, i2Representing transmit loop current transients, dlR-zRRepresenting an intermediate variable, dlR _ zR＝dlxR*RyR-dlyR*RxR，dlxRRepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-component, Ry, of a differential current element on the receiving coilRRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, RxRRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000223
represents the distance between the middle point of the ith segment of current element in the jth turn coil of the receiving coil and the observation plane point G of the receiving coil,
the magnetic field in the z-axis direction generated at point G by the j-th turn receive coil and the N-th turn receive coil can be calculated.
Figure GDA0003440087330000224
Wherein the content of the first and second substances,
Figure GDA0003440087330000225
represents the magnetic field, mu, generated by the j-th turn and the i-th section of current element in the receiving coil at the observation plane point G of the receiving coil along the Z-axis direction0Denotes the magnetic permeability in vacuum, i1Representing transmit loop current transient, dlR _ zRRepresenting an intermediate variable, dlR _ zR＝dlxR*RyR-dlyR*RxR，dlxRRepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-component, Ry, of a differential current element on the receiving coilRRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, RxRThe component of the differential current element pointing to the center of the small observation circle along the direction of the x axis is shown, i is a variable i is 1,2, …, Nh，
Figure GDA0003440087330000226
Represents the distance between the middle point of the ith segment of current element in the jth turn coil of the receiving coil and the observation plane point G of the receiving coil,
Figure GDA0003440087330000227
Figure GDA0003440087330000228
i represents the magnetic induction intensity of the N turns of coils generated at the point G along the Z-axis direction, and the variable i is 1,2, …, NhJ is variable j ═ 1,2, …, N, μ0Denotes the magnetic permeability in vacuum, i2Representing the receive loop current transient, dlR _ zRRepresenting an intermediate variable, dlR _ zR＝dlxR*RyR-dlyR*RxR，dlxRRepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-component, Ry, of a differential current element on the receiving coilRRepresenting the component of the differential current element pointing to the centre of the small observation circle along the y-axis, RxRRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000231
the distance between the middle point of the ith section of current element in the jth turn coil of the receiving coil and the observation plane point G of the receiving coil,
calculating the magnetic flux of the transmitting coil on the small circle of the observation plane, and obtaining the magnetic flux in the z-axis direction in the small circle of the observation plane according to a uniform magnetic field magnetic flux calculation formula phi (BS)
Figure GDA0003440087330000232
Wherein the content of the first and second substances,
Figure GDA0003440087330000233
the magnetic induction intensity along the Z-axis direction generated by the N turns of coils at the point G is shown, R represents the radius of the coils, l represents the number of the division sections of the radius of the coils,
the total flux of the transmitter coil can then be expressed as:
Figure GDA0003440087330000234
wherein, phi RT represents the magnetic flux generated by the transmitting coil on the whole observation plane of the receiving coil, g is a variable h which is 1,2,3, m, m represents the number of observation subunits,
Figure GDA0003440087330000235
representing the magnetic flux in the direction of the z axis in a small circle of the observation plane;
the induction voltage u of the transmitting coil can be obtained by replacing the formula (38) with the formula (17)12。
Figure GDA0003440087330000237
Wherein u is12Indicating the induced voltage, mu, of the transmitting coil0Denotes the vacuum permeability, ω denotes the angular velocity, σ denotes the electrical conductivity, N denotes the number of coil turns, R denotes the coil radius, I2mThe maximum value of the current of the receiving coil is shown, l represents the number of coil radius dividing sections, and i is a variable i is 1,2, …, Nh，NhThe number of evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, g is a variable h which is 1,2,3RR represents an intermediate variable, and R represents a variable,
Figure GDA0003440087330000236
dlxRrepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-component, Ry, of a differential current element on the receiving coilRRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, RxRRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure GDA0003440087330000241
the distance between the middle point of the ith section of current element in the jth turn coil of the receiving coil and the observation plane point G of the receiving coil.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.

Claims (7)

1. A method for determining the power transmission efficiency of a magnetic resonance type wireless electric energy transmission system is characterized by comprising the following steps: the method comprises the following steps:
the power transmission efficiency eta of the wireless electric energy transmission system is determined by adopting the following method:
Figure FDA0003440087320000011
where eta represents transmission efficiency, PoutRepresenting output power, PinRepresents the input power;
the output power PoutIs determined by simultaneous equations (2) and (3):
Figure FDA0003440087320000012
wherein, PoutDenotes the output power, I2Representing the effective value of the current in the receiving loop, RLRepresenting the receiver coil load, mu0Denotes the vacuum permeability, ω denotes the angular velocity, σ denotes the electrical conductivity, N denotes the number of coil turns, R denotes the coil radius, a denotes the coil wire diameter, I1mDenotes the maximum value of the primary coil current, l denotes the number of coil radius divisions, and i is a variable of 1,2, …, Nh，NhThe number of the evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, h is a variable h which is 1,2,3, wherein m is the number of observation subunits, dlR _ Z is the number of observation subunits, andTrepresenting an intermediate variable, dlR _ ZT＝dlxT*RyT-dlyT*RxTWherein, dlxTRepresenting the x-component, Ry, of a differential current element on the transmitting coilTRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, dlyTRepresenting the y-component of a differential current element on the transmitting coil, RxTThe component of the differential current element pointing to the center of the small observation circle along the direction of the x axis is shown, the j-th turn in the transmitting coil and the magnetic field generated by the i-th section of the current element at the observation plane point H of the receiving coil are shown,
Figure FDA0003440087320000013
representing the distance between the midpoint of the ith section of current element in the jth turn coil of the transmitting coil and the observation plane point H of the receiving coil;
wherein the input power PinIs determined by simultaneous equations (4) and (5):
Figure FDA0003440087320000021
wherein，PinRepresenting input power, U1Representing the effective value of the voltage of the transmission loop, I1Representing the effective value of the current of the transmission loop, mu0Denotes the vacuum permeability, ω denotes the angular velocity, σ denotes the electrical conductivity, N denotes the number of coil turns, R denotes the coil radius, a denotes the coil wire diameter, I2mThe maximum value of the current of the receiving loop is shown, l represents the number of coil radius dividing sections, and i is a variable i is 1,2, …, Nh，NhThe number of the evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, g is a variable g which is 1,2,3, m is the number of observation subunits, dlR _ Z is the number of observation subunits, andRrepresenting an intermediate variable, dlR _ ZR＝dlxR*RyR-dlyR*RxR，dlxRRepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-component, Ry, of a differential current element on the receiving coilRRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, RxRRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure FDA0003440087320000022
the distance between the middle point of the ith segment of current element in the jth turn coil of the receiving coil and the observation plane point G of the receiving coil is shown.
2. The method for determining the power transmission efficiency of a magnetic resonance type wireless power transmission system according to claim 1, wherein: receiving a return current I2Determined by simultaneous equations (6) to (11),
Figure FDA0003440087320000023
wherein, I2Representing the effective value of the current of the receiving loop, I2mRepresenting the maximum value of the current of the receiving loop circuit;
Figure FDA0003440087320000024
wherein, I2mIndicating the maximum value of the current in the receiving loop, i2Representing the receive loop current transient, ω representing angular velocity,
Figure FDA0003440087320000025
represents a phase angle;
Figure FDA0003440087320000026
wherein i2Representing instantaneous value of current, u, of receiving loop2Representing instantaneous value of the voltage of the receiving loop, RΩThe resistance of the ohmic losses is expressed in terms of,
Figure FDA0003440087320000031
wherein, mu0Denotes the vacuum permeability, ω denotes the angular velocity, σ denotes the electrical conductivity, a denotes the coil wire diameter, N denotes the number of coil turns, R denotes the coil radius, R denotes the coil wire diameterLRepresenting the receive coil load;
Figure FDA0003440087320000032
wherein u is2Representing instantaneous value of the voltage of the receiving loop, N2Indicating the number of receiver coil turns, where N2＝N，φ21Represents the current i1A generated magnetic flux passing perpendicularly through the receiving coil;
φ21≈φTR (10)
wherein phi is21Represents the current i1The generated magnetic flux, phi, passing perpendicularly through the receiving coilTRRepresenting the receiver coil viewing plane magnetic flux;
Figure FDA0003440087320000033
wherein phi isTRDenotes the flux of the receiver coil in the observation plane, N denotes the number of turns of the coil, dlR-ZTExpressed as an intermediate variable, R represents the coil radius, l represents the number of coil radius divisions, and i is a variable i-1, 2, …, Nh，NhThe number of the evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, h is a variable h which is 1,2,3, wherein m is the number of observation subunits, dlR _ z is representedTRepresenting an intermediate variable, dlR _ zT＝dlxT*RyT-dlyT*RxTWherein, dlxTRepresenting the x-component, Ry, of a differential current element on the transmitting coilTRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, dlyTRepresenting the y-component of a differential current element on the transmitting coil, RxTRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure FDA0003440087320000034
the distance between the middle point of the ith section of current element in the jth turn coil of the transmitting coil and the observation plane point H of the receiving coil is shown.
3. The method for determining the power transmission efficiency of a magnetic resonance type wireless power transmission system according to claim 2, wherein: the receiving coil observes a planar flux phiTRObtained by the following method:
s1: establishing a cylindrical spiral resonance coil analysis model under a three-dimensional rectangular coordinate system; the central axis of the transmitting coil and the central axis of the receiving coil are coincided with the Z axis, wherein the center of the circle of the bottom surface of the transmitting coil is coincided with the far point of the coordinate axis, and the receiving coil is positioned above the transmitting coil and is positioned at the position D;
s2: dividing each turn of transmitting coil into NhA segment;
s3: determining an observation plane; the cross section of the coil in the middle is an observation plane;
s4: drawing an observation subunit on the observation plane;
s5: calculating the magnetic flux generated by the transmitting coil in the observation subunit
Figure FDA0003440087320000045
Figure FDA0003440087320000041
Wherein the content of the first and second substances,
Figure FDA0003440087320000046
the magnetic flux generated by the transmitting coil in the observation subunit is shown, R represents the coil radius, l represents the number of coil radius division segments, and i is the variable i is 1,2, …, Nh，NhThe number of the evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, h is a variable h which is 1,2,3, wherein m is the number of observation subunits, dlR _ z is representedTRepresenting an intermediate variable, dlR _ zT＝dlxT*RyT-dlyT*RxTWherein, dlxTRepresenting the x-component, Ry, of a differential current element on the transmitting coilTRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, dlyTRepresenting the y-component of a differential current element on the transmitting coil, RxTRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure FDA0003440087320000042
representing the distance between the midpoint of the ith section of current element in the jth turn coil of the transmitting coil and the observation plane point H of the receiving coil;
s6: the magnetic flux generated by the transmitter coil in the observation plane is calculated.
4. The method for determining the power transmission efficiency of a magnetic resonance type wireless power transmission system according to claim 3, wherein: the step S4 of drawing an observation subunit on the observation plane includes the steps of:
s41: equally dividing the radius of the coil into l sections;
s42: using the center of a circle of the observation plane as the center of a circle
Figure FDA0003440087320000043
Drawing concentric circles for the radius, wherein R denotes the coil radius, l denotes the number of coil radius divisions, and k denotes a variable, wherein k is 1,3,5 … (l-1);
s43: the center of the observation subunit is positioned on the circumference of the concentric circle, so as to
Figure FDA0003440087320000044
Drawing observation subunits, wherein every two observation subunits are tangent, wherein R represents the radius of the coil, and l represents the number of coil radius division sections;
s44: step S43 is repeated until the observation plane cannot draw an observation subunit satisfying step S43.
5. The method for determining the power transmission efficiency of a magnetic resonance type wireless power transmission system according to claim 1, wherein: the effective value U1 of the transmitting loop voltage is obtained by the following method:
U1＝U11+U12 (13)
wherein, U1Representing the effective value of the voltage of the transmission loop, U11Indicating the value of the voltage, U, generated by the transmitting coil itself12Representing the induced voltage of the receiving coil to the transmitting coil,
U11＝I1RΩ (14)
wherein, U11Representing the value of the voltage generated by the transmitting coil itself, I1Representing the effective value of the current of the transmitting loop, RΩThe resistance of the ohmic losses is expressed in terms of,
Figure FDA0003440087320000051
wherein, mu0Denotes the vacuum permeability, ω denotes the angular velocity, σ denotes the electrical conductivity, N denotes the number of coil turns, R denotes the coil radius,
Figure FDA0003440087320000052
wherein, U12Indicating the induced voltage of the receiving coil to the transmitting coil, U12mRepresents the maximum value of the induced voltage of the receiving coil to the transmitting coil,
Figure FDA0003440087320000053
wherein, U12mRepresenting the maximum value of the induced voltage, U, of the receiving coil to the transmitting coil12Representing the induced voltage of the receiver coil to the transmitter coil, omega representing the angular velocity,
Figure FDA0003440087320000055
represents a phase angle;
Figure FDA0003440087320000054
wherein, U12Representing the induced voltage of the receiving coil to the transmitting coil, N1Indicating the number of transmitter coil turns, where N1＝N2＝N，φ12Representing the magnetic flux generated by the receiver coil at the transmitter coil;
φ12≈φRT (18)
wherein phi is12Representing the magnetic flux generated by the receiver coil at the transmitter coil; phi is aRTRepresenting the transmitter coil observation plane magnetic flux;
Figure FDA0003440087320000061
wherein phi isRTDenotes the magnetic flux of the observation plane of the transmitting coil, R denotes the coil radius, l denotes the number of coil radius divisions, and i is a variable of 1,2, …, Nh，NhThe average number of divided sections of each turn of the transmitting coil is represented, j is variable j is 1,2, …, N represents the number of turns of the coil, and g isThe variable g is 1,2, 3., m, m denotes the number of observed subunits, dlR _ zRRepresenting an intermediate variable, dlR _ ZR＝dlxR*RyR-dlyR*RxR，dlxRRepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-component, Ry, of a differential current element on the receiving coilRRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, RxRRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure FDA0003440087320000062
the distance between the middle point of the ith segment of current element in the jth turn coil of the receiving coil and the observation plane point G of the receiving coil is shown.
6. The method for determining the power transmission efficiency of a magnetic resonance type wireless power transmission system according to claim 5, wherein: the transmitting coil observes a planar magnetic flux phiRTObtained by the following method:
s1: establishing a cylindrical spiral resonance coil analysis model under a three-dimensional rectangular coordinate system; the central axis of the transmitting coil and the central axis of the receiving coil are coincided with the Z axis, wherein the center of the circle of the bottom surface of the transmitting coil is coincided with the far point of the coordinate axis, and the receiving coil is positioned above the transmitting coil and is positioned at the position D;
s2: dividing each turn of receiving coil into NhA segment;
s3: determining an observation plane; the cross section of the middle part of the transmitting coil is an observation plane;
s4: drawing an observation subunit on the observation plane;
s5: calculating the magnetic flux generated by the transmitting coil in the observation subunit
Figure FDA0003440087320000064
Figure FDA0003440087320000063
Wherein the content of the first and second substances,
Figure FDA0003440087320000071
the magnetic flux generated by the receiving coil in the observation subunit is shown, R represents the coil radius, l represents the number of coil radius division segments, and i is a variable i is 1,2, …, Nh，NhThe number of the evenly divided sections of each turn of the transmitting coil is represented, j is a variable j which is 1,2, …, N is the number of turns of the coil, g is a variable g which is 1,2,3, m is the number of observation subunits, dlR _ Z is the number of observation subunits, andRrepresenting an intermediate variable, dlR _ ZR＝dlxR*RyR-dlyR*RxR，dlxRRepresenting the x-axis component, dly, of a differential current element on the receiving coilRRepresenting the y-component, Ry, of a differential current element on the receiving coilRRepresenting the component of the differential current element pointing to the centre of the small observation circle in the direction of the y-axis, RxRRepresenting the component of the differential current element pointing to the center of the small observation circle along the direction of the x axis,
Figure FDA0003440087320000072
representing the distance between the midpoint of the ith section of current element in the jth turn coil of the receiving coil and the observation plane point G of the receiving coil;
s6: the magnetic flux generated by the transmitter coil in the observation plane is calculated.
7. The method for determining the power transmission efficiency of a magnetic resonance type wireless power transmission system according to claim 6, wherein: the step S4 of drawing an observation subunit on the observation plane includes the steps of:
s41: equally dividing the radius of the coil into l sections;
s42: using the center of a circle of the observation plane as the center of a circle
Figure FDA0003440087320000073
Drawing concentric circles for the radius, wherein R denotes the coil radius, l denotes the number of coil radius divisions, and k denotes a variable, wherein k is 1,3,5 … (l-1);
s43: with said observation subunitThe center of the circle is positioned on the circumference of the concentric circle so as to
Figure FDA0003440087320000074
Drawing observation subunits, wherein every two observation subunits are tangent, wherein R represents the radius of the coil, and l represents the number of coil radius division sections;
s44: step S43 is repeated until the observation plane cannot draw an observation subunit satisfying step S43.
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