Design of Magnetic Coupler for Wireless Power Transfer

energies

Article Design of Magnetic Coupler for Wireless Power Transfer

Heqi Xu , Chunfang Wang *, Dongwei Xia and Yunrui Liu College of Electrical Engineering, Qingdao University, Qingdao 266071, China * Correspondence: [email protected]; Tel.: +86-158-9887-1588

Received: 13 July 2019; Accepted: 1 August 2019; Published: 3 August 2019

Abstract: In order to improve the restraint ability of electromagnetic energy in space and improve the coupling efficiency, a magnetic coupler structure with composite magnetic shield is proposed. Firstly, the model is established by using the finite-element simulation software. Then, according to the limit of public exposure to time-varying electromagnetic fields pointed out in ICNIPR (International Commission on Non-Ionizing Radiation Protection) guidelines, the characteristics and spatial magnetic field distribution of magnetic couplers with a single shielding structure, double shielding structure, and composite shielding structure are compared and analyzed. Finally, the experimental results show that the structure of magnetic couplers with a composite magnetic shield has a good effect in strengthening magnetic field concentration and reducing the electromagnetic interference of wireless charging systems to the external environment. It also has the advantages of smaller volume, lighter weight, and lower cost, and can effectively improve the transmission efficiency and enhance the stability of wireless charging systems.

Keywords: wireless power transfer; magnetic shield; coupling coeﬃcient; magnetic coupler

1. Introduction Wireless power transfer (WPT) is a system that uses a high-frequency electromagnetic field to transmit energy in space. It is more convenient and safer since it does not need cables and bolts [1]. Magnetic flux leakage in WPT will not only harm the human body, but also interfere with other electronic devices. At the same time, it will reduce the coupling coefficient and the system power [2,3]. Therefore, in order to reduce the effect of magnetic flux leakage from WPT system and improve the coupling coefficient, it is very necessary to design of the magnetic coupler. The basic magnetic coupling is composed of a receiving coil and a transmitting coil. In order to improve the coupling coefficient and reduce the power loss, a ferrite core is usually added around the magnetic coupler to restrain the electromagnetic field around the magnetic coupler. Many studies have been done to improve the coupling coefficient of WPT systems. One type of study is to add ferrite cores around the magnetic coupler and optimize it by changing the shape of ferrite cores. The authors of [4] presented a square-embedded cross-shaped ferrite core structure for DLDD (Double Layer Double D-type) coils, which could satisfy the requirements of mutual inductance design and reduces the amount of ferrite. The authors of [5] designed and compared five different magnetic-core distribution schemes for circular pads in the wireless charging systems of electric vehicles. After considering power factor and volume of the magnetic coupler, the optimal structure was obtained. The authors of [6] presented a new design method of WPT coil shielding structure based on magnetic field characteristics of helical coils. A shielding structure called enhanced fans-shape was established, and the simulation and experimental results showed that the new structure can effectively reduce the volume of the magnetic coupler. However, it did not take into account the manufacturing process and fragile properties of ferrite. In the work cited in [7], the expressions of equivalent magnetic

Energies 2019, 12, 3000; doi:10.3390/en12153000 www.mdpi.com/journal/energies Energies 2019, 12, x FOR PEER REVIEW 2 of 12 structure was designed and optimized for DD coil, which effectively improved the coupling coefficient. There are also many studies that have used thin metal plates to shield high-frequency electromagnetic fields. The authors of [8] studied the effect of metal shielding by changing the geometricEnergies structure2019, 12 ,of 3000 metal plate and the coupling condition of WPT and explored the2 application of 12 of the best shielding method of metal plate in WPT systems. There are also many other types of shielding structures for reference in this paper [9–12]. circuits and coupling coefficients were deduced. A new core structure was designed and optimized for At present,DD coil, whichthe shielding effectively of improved magnetic the couplingcouplers coe isffi generallycient. There divided are also manyinto single studies ferrite that have shield or double shieldused thin composed metal plates of toa shieldferrite high-frequency and an aluminum electromagnetic plate. fields. It has The many authors problems, of [8] studied such the as high magnetice ffenergyect of metal loss, shielding unsatisfactory by changing shielding the geometric effect, structure relatively of metal low plate efficiency, and the coupling and high condition cost. In this paper, basedof WPT on and the explored principle the applicationof inductively of the bestcoupled shielding wireless method ofpower metal platetransfer in WPT (ICPT) systems. system, a magneticThere coupler are also structure many other with types small of shielding size, structureslight weight, for reference low cost, in this and paper good [9–12 ].shielding effect is At present, the shielding of magnetic couplers is generally divided into single ferrite shield proposed.or The double influence shield composed of composite of a ferriteshielding and anon aluminum the magnetic plate. field It has distribution many problems, around such the as energy transfer mechanismhigh magnetic is energy calculated loss, unsatisfactory by finite elem shieldingent simulation effect, relatively and low compared efficiency, with and high the cost.traditional shieldingIn structure, this paper, basedwhich on verifies the principle the ofrationality inductively of coupled the design wireless structure. power transfer In the (ICPT) experiment, system, it is found thata magneticthe magnetic coupler coupler structure structure with small with size, composite light weight, magnetic low cost, andshield good not shielding only strengthens effect is the magneticproposed. field concentration The influence ofin composite the energy shielding transf on theer magneticarea, but field also distribution reduces around the theelectromagnetic energy transfer mechanism is calculated by finite element simulation and compared with the traditional radiationshielding in the nonenergy structure, which transmission verifies the rationalityarea, whic ofh the has design higher structure. transmission In the experiment, efficiency it isthan the traditionalfound shielding that the structure. magnetic coupler structure with composite magnetic shield not only strengthens the magnetic field concentration in the energy transfer area, but also reduces the electromagnetic radiation 2. Shieldingin the Structure nonenergy Design transmission of Magnetic area, which Coupler has higher transmission efficiency than the traditional shielding structure. Figure 1 is the schematic diagram of the inductively coupled wireless power transfer system. When the2. system Shielding is Structure working, Design the ofpower Magnetic frequency Coupler alternating current (AC) of the power grid is converted toFigure DC 1by is therectification schematic diagram and filtering, of the inductively and then coupled converted wireless powerto high transfer frequency system. AC by high-frequencyWhen the systeminverter. is working, After thereactive power frequency power alternating compensation, current (AC) the of thehigh-frequency power grid is converted alternating magneticto field DC byis generated rectification in and the filtering, transmitting and then co convertedil. The high-frequency to high frequency alternating AC by high-frequency magnetic field is inverter. After reactive power compensation, the high-frequency alternating magnetic field is generated coupled into the the transmitting receiving coil. coil The to high-frequency generate indu alternatingction magneticvoltage, field then, is coupled though to the the receiving reactive coil power compensationto generate network, induction the voltage, DC or then, AC thoughpower the is reactiveoutputted power through compensation rectifier network, filter the circuit DC or or AC rectifier filter inverterpower circuit is outputted to supply through for rectifier the load filter an circuitd realize or rectifier wireless filter inverter transm circuitission to of supply energy for the [13]. load and realize wireless transmission of energy [13].

Shielding Magnetic Coupler Shielding

Rectifier Rectifier and Power Grid L L and Filter Inverter Uin P S AC in Circuit CircuIt R RP RS L Electromagnetic Reactive Field Reactive Power Power load Compensation Compensation Network Network Figure 1. The schematic diagram of the inductively coupled wireless power transfer (WPT) system. Figure 1. The schematic diagram of the inductively coupled wireless power transfer (WPT) system. Parallel–series topologies are adopted in this circuit—transmitting coil and compensation network Parallel–seriesare in parallel; topologies and the receiving are adopted coil and compensationin this circuit—transmitting network are in series. Incoil Figure and1 , compensationLP and LS are the inductance of transmitting coil and receiving coil. RP and RS are the internal resistance network are in parallel; and the receiving coil and compensation network are in series. In Figure 1, LP of transmitting coil and receiving coil. Uin is the output voltage of electric energy after rectiﬁcation and LS areand the high-frequency inductance of inversion. transmittingM is the coil mutual and inductance receiving between coil. RP transmitting and RS are coil the and internal receiving resistance of transmittingcoil. k is coil the couplingand receiving coeﬃcient. coil.RL Uisin the is loadthe resistance.output voltageIL is the of current electric of R Lenergy. IP is the after current rectification of and high-frequency inversion. M is the mutual inductance between transmitting coil and receiving coil. k is the coupling coefficient. RL is the load resistance. IL is the current of RL. IP is the current of the transmitting coil, QP and QS are the quality factor of the primary and secondary circuit. η is the efficiency of the wireless charging system. In the case of full reactive power compensation, the output power PO of the system can be expressed in Equation (1) [14, 15].

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2 22M Energies 2019, 12, 3000 POLSPS== I Q Uin I k Q 3 of 12(1) LS Energies 2019, 12, x FOR PEER REVIEW 3 of 12

the transmitting coil, QP and QS are the qualityM factor of the primary and secondary circuit. η is the k = 2 (2) efficiency of the wireless charging system. In22 theM case of full reactive power compensation, the output P== ILLPS Q U I k Q (1) power PO of the system can be expressedOLSPS in Equation (1)in [14,15]. LS ωM1 2 P = I 2 MQ = U I k2Q (1) O kL =1L S in P S (2) (3) S +1 LLPS k QPS Q M k = (2) 1√LPL According to Equations (1) and (3), = it is obviousS that the output power increases with the 1 1 (3) coupling coefficient, and the efficiency of η the= wireless+1 charging system is also influenced by(3) the k Q Q1 coupling coefficient. The mutual inductance andPS coupling+ 1 factor between the coils can be changed k √QPQS by changingAccording the design to Equationof the magnetics (1) and structure (3), it is obviousof the magnetic that the coupler. output power increases with the According to Equations (1) and (3), it is obvious that the output power increases with the coupling Takingcoupling the coefficient, flat disk magnetic and the efficiency coupler as of an the example, wireless chargingthe flat disk system mag isnetic also coupler influenced can bygenerate the coefficient, and the efficiency of the wireless charging system is also influenced by the coupling coupling coefficient. The mutual inductance and coupling factor between the coils can be changed a uniformcoefficient. magnetic The mutual field inductance in the energy and coupling transfer factor area. between In order the coils to can reduce be changed the magnetic by changing field by changing the design of the magnetic structure of the magnetic coupler. distributionthe design in the of the nonworking magnetic structure area and of the enhance magnetic the coupler. magnetic field concentration in the working Taking the flat disk magnetic coupler as an example, the flat disk magnetic coupler can generate area, the magneticTaking the coupler flat disk is magnetic usually coupler designed. as an For example, magnetic the flat couplers disk magnetic with shielding, coupler can the generate traditional a a uniform magnetic field in the energy transfer area. In order to reduce the magnetic field ICPT uniform shielding magnetic structure field is in dividedthe energy into transfer single area. shield In order and to double reducethe shielding, magnetic thatfield distribution is, single shield in distribution in the nonworking area and enhance the magnetic field concentration in the working composedthe nonworking of ferrite or area double and enhance shield the composed magnetic of field a concentrationferrite and an in aluminum the working plate. area, theThe magnetic schematic area, the magnetic coupler is usually designed. For magnetic couplers with shielding, the traditional diagramcoupler is shown is usually in Figure designed.s 2 and For 3. magnetic couplers with shielding, the traditional ICPT shielding ICPT shielding structure is divided into single shield and double shielding, that is, single shield structure is divided into single shield and double shielding, that is, single shield composed of ferrite composed of ferrite or double shield composed of a ferrite and an aluminum plate. The schematic or double shield composed of a ferrite and an aluminum plate. The schematic diagram is shown in diagram is shown in Figures 2 and 3. Figures2 and3. Receiving coil Ferrite Air gap ReceivingTransmitting coil Ferrite Air gap coil Transmitting coil Figure 2. Cross-section view of single shield magnetic coupler. Figure 2. Cross-section view of single shield magnetic coupler. Figure 2. Cross-section view of single shield magnetic coupler. Aluminum sheet Receiving coil Ferrite Aluminum sheet Air gap ReceivingTransmitting coil Ferrite Air gap Transmittingcoil Aluminumcoil sheet Aluminum sheet Figure 3. Cross-section view of double shield magnetic coupler of WPT system. Figure 3. Cross-section view of double shield magnetic coupler of WPT system. When theFigure ferromagnetic 3. Cross-section material viewexists, of double the shield self-inductance magnetic couplerL of of the WPT resonator system. coil increases, Whenthe resonance the ferromagn frequencyeticf materialdecreases, exists, and the the maximum self-inductance transmission L of the effi resonatorciency point coil of increases, the system the When the ferromagnetic material exists, the self-inductance L of the resonator coil increases, the resonanceshifts frequency to the left (the f decreases, frequency and decreases). the maximum At the same transmission time, due toefficiency the increase point of Mof, the the system maximum shifts resonance frequency f decreases, and the maximum transmission efficiency point of the system shifts efficiency of the system also increases to a certain extent. At this time, if the switching frequency of the to theto left the (the left (thefrequency frequency decreases). decreases). At At the the same same time, time, due due to the the increas increase e of of M M, the, the maximum maximum power supply at the transmitter is unchanged, the transmission efficiency will be reduced. In light-load efficiencyefficiency of the of system the system also also increases increases to toa certaina certain extent. extent. AtAt thisthis time, if if the the switching switching frequency frequency of of systems, if the resonators are over-coupled, frequency splitting will occur, which will reduce the the powerthe power supply supply at the at thetransmitter transmitter is isunchanged, unchanged, the the transmissiontransmission efficiencyefficiency will will be be reduced. reduced. In In overall output power of the system. When the non-ferromagnetic aluminum plate exists, the eddy light-loadlight -load systems, systems, if the if the resona resonatorstors are are over over-coupled,-coupled, frequency frequency splitting splitting will will occur, occur, which which will will current generated in the aluminum plate produces a reverse magnetic field, which counteracts with the reducereduce the overall the overall output output power power of theof the system. system. When When the the nonnon-ferromagnetic aluminum aluminum plate plate exists, exists, magnetic field of the emission source and plays a shielding role. At this time, the self-inductance L of the eddy current generated in the aluminum plate produces a reverse magnetic field, which the eddythe resonator current coil generated decreases, in the the mutual aluminum inductance plateM of produces the system aweakens, reverse the magnetic resonance field, frequency which counteracts with the magnetic field of the emission source and plays a shielding role. At this time, counteractsf of the with system the increases, magnetic and field the maximumof the emission transmission source e ffiandciency plays point a shielding of the system role. shifts At this to the time, the self-inductance L of the resonator coil decreases, the mutual inductance M of the system the selfright.-inductance For this reason, L of the the combination resonator of coil shielding decreases, materials the should mutual be considered inductance in combinationM of the with system weakens,weakens, the resonance the resonance frequency frequency f off of the the system system increases, increases, and and the the maximum maximum transmission transmission efficiency point of the system shifts to the right. For this reason, the combination of shielding efficiency point of the system shifts to the right. For this reason, the combination of shielding materials should be considered in combination with the resonant frequency of the magnetic coupler, materials should be considered in combination with the resonant frequency of the magnetic coupler,

Energies 2019, 12, x FOR PEER REVIEW 4 of 12 the switching frequency of the transmitting circuit, the transmitting frequency of the harmonic wave and the coupling coefficient. Therefore, a new type of magnetic coupler with multilayered shielding structureEnergies is2019 proposed, 12, 3000 , as shown in Figure 4. 4 of 12 Energies 2019, 12, x FOR PEER REVIEW 4 of 12

thethe resonantswitching frequency frequency of of the the magnetic transmitting coupler, circuit, the the switching transmitting frequency frequency of the Aluminumof transmitting the harmonic circuit,foil wave theand transmitting the coupling frequency coefficient. of Therefore, the harmonic a new wave type and of themagnetic coupling coupler coeffi cient.with multilayeredNanocrystalline Therefore, a newshielding type ofstructure magnetic is proposed coupler with, as shown multilayered in Figure shielding 4. structure is proposed, as shown in Figurestrip4. Aluminum foil Ferrite Air gap ReceivingNanocrystalline coil Transmittingstrip coil Ferrite Air gap Receiving coil Figure 4. Cross-section view of composite shield magnetic couplerTransmitting of WPT system . coil The first layer of the shield layer on the receiving coil side of the magnetic coupler shown in Figure 4. Cross-section view of composite shield magnetic coupler of WPT system. Figure 4 is a ferriteFigure sheet, 4. Cross the-section second view layerof composite is a nanocrystallineshield magnetic coupler strip, of WPT and system the third. layer is an aluminumThe foil. first Ferrite layer is of used the shieldto shield layer electromagnetic on the receiving waves coil side of the of thekHz magnetic level. The coupler thickness shown of the iron-basedin FigureThe nanocrystalline 4first is alayer ferrite of sheet,the strip shield the is only secondlayer 26 on layerμm, the receivingthe is a resistivity nanocrystalline coil side is onlyof strip,the 137 magnetic and μΩ∙cm, the coupler third and layerthe shown saturation is an in magnetialuminumFigurec induction 4 is foil. a ferrite Ferrite is as sheet,high is used as the to1.6 secondshield T [16] electromagnetic layer. The is aluminum a nanocrystalline waves foil of is the used strip, kHz for level.and high the The- frequency third thickness layer ofmagneticis the an iron-basedaluminum foil. nanocrystalline Ferrite is used strip to isshield only electromagnetic 26 µm, the resistivity waves is of only the 137kHzµ level.Ω cm, The and thickness the saturation of the field components that are not shielded from the first and second low-reluctance· circuits. In real life, magneticiron-based induction nanocrystalline is as high strip as is 1.6 only T [16 26]. μm, The the aluminum resistivity foil is is only used 137 for μΩ∙cm, high-frequency and the saturation magnetic the transmittingmagnetic induction coil isis as generally high as 1.6 buried T [16] . deepThe aluminum under thefoil is bottom used for or high fixed,-frequency so the magnetic shielding requiremfieldent components of the transmitting that are not shieldedcoil side fromis low, the while first and the second receiving low-reluctance side is usually circuits. moved. In real In life, order thefield transmitting components coil that is generallyare not shielded buried from deep underthe first the and bottom second or low fixed,-reluctance so the shielding circuits. requirement In real life, to save space and reduce the volume of the equipment, the receiving circuit board will be placed ofthe the transmitting transmitting coil coil sideis generally is low, while buried the receiving deep under side the is usually bottom moved. or fixed, In order so the to save shielding space above the receiving coil, so the shielding requirement on the receiving side is higher. andrequirem reduceent the of volumethe transmitting of the equipment, coil side theis low, receiving while circuit the receiving board will side be is placed usually above moved. the receiving In order coil,to save so thespace shielding and reduce requirement the volume on the of receiving the equipment, side ishigher. the receiving circuit board will be placed 3. Magneticabove the Coupler receiving Structure coil, so the shielding requirement on the receiving side is higher. 3. Magnetic Coupler Structure In3. Magneticthis paper, Coupler a three Structure-dimensional structure model of magnetic coupling for the small fruit and vegetableIn juicer this paper, is established. a three-dimensional As shown structure in Figure model 5, of coil magnetic parameters coupling are for shown the small in T fruitable and 1; and In this paper, a three-dimensional structure model of magnetic coupling for the small fruit and shieldingvegetable geometry juicer is parameters established. are As shownshown in in Figure Table5, coil2. parameters are shown in Table1; and shielding geometryvegetable parametersjuicer is established. are shown As in Tableshown2. in Figure 5, coil parameters are shown in Table 1; and shielding geometry parameters are shown in Table 2. Nanocrystalline Aluminum foil 136mm Nanocrystalline Aluminum foil 136mm 27mm 54mm 27mm Ferrite E 54mm Ferrite E Receiving coil Ferrite A Receiving coil Ferrite A Transmitting Ferrite D Transmittingcoil Ferrite D coil Ferrite B Ferrite B

Ferrite CC Figure 5. A 3D structure model of magnetic coupling for the small fruit and vegetable juicer.

FigureFigure 5. A 5.3D A structure3D structure model model of ofmagnetic magnetic coupling coupling for thethe s smallmall fruit fruit and and vegetable vegetable juicer juicer. .

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Table 1. Parameter of the coil.

Parameter data Outer-diameter of transmitting coil 122 mm Energies 2019, 12, x FOR PEER REVIEWInner- diameter of transmitting coil 42 mm 5 of 12 Energies 2019 12 , , 3000 Outer-diameter of receiving coil 37 mm 5 of 12 Table 1. Parameter of the coil. Inner-diameter of receiving coil 16 mm Parameter Data LengthTable of receiving 1. Parameter coil of the coil. 54 mm Outer-diameter of transmitting coil 122 mm Parameter Data Inner-diameterTurns of transmitting of transmitting coil coil 42 mm 28 Outer-diameterTurns of receiving of of transmitting receiving coil coil 37 122 mm mm 30 Inner-diameterInner-diameterTransmission of of transmitting receiving distance coil 16 42 mm mm18 mm Outer-diameter of receiving coil 37 mm Inner-diameterLength of receiving of receiving coil coil 54 16 mm mm Table 2.Turns GLengtheometry of oftransmitting receiving parameter coil coils of shielding 54 28 mmmaterial. Turns of of transmitting receiving coil coil 30 28 MaterialTransmissionTurns of receiving distanceSize/mm coil 18Number mm 30 Transmission distance 18 mm Ferrite A 10*5*19 4 Table 2. Geometry parameters of shielding material. TableFerrite 2. Geometry B parameters51*17*5 of shielding material.6 Material Size/mm Number Ferrite C 12*5*15 6 MaterialFerrite A Size10*5*19/mm Number 4 FerriteFerriteFerrite A DB 51*17*5 10*5*1951*5*19 6 4 2 Ferrite B 51*17*5 6 FerriteFerrite EC 12*5*15• 6 1 Ferrite C 12*5*15 6 NanocrystallineFerriteFerrite D D 51*5*19 51*5*19 2 2 1 • AluminumFerriteFerrite E E foil 1 1 1 Nanocrystalline 1 1 Aluminum foil 1 Aluminum foil 1 Based on the field conditions satisfied by the working area of the energy transfer mechanism, a three-dimensionalBasedBased on on finitethe the field field element conditions conditions simulation satisfied satisfied by analysis bythe the wo workingrking is performed area area of the of theenergy to energy obtain transfer transfer a magnetic mechanism, mechanism, flux a density distributionthree-dimensionala three-dimensional diagram, finiteas finite shown element element simulation in simulation Figure analysis 6. analysis It isillustrates performed is performed to that toobtain obtain the a magnetic double a magnetic flux shielding flux density density structure effectivelydistributiondistribution reduces diagram, diagram, the distribution as shownshown in ofin Figure theFigure 6nonworking. It6. illustrates It illustrates thatarea, the that while double the thedouble shielding magnetic shielding structure field structure e ff ofectively the working reduces the distribution of the nonworking area, while the magnetic field of the working area is also area is effectivelyalso reduced. reduces For the thedistribution composite of the s nonworkihieldingng structure, area, while the the magnetic field field of the of workingthe nonworking areareduced. is also Forreduced. the composite For the shieldingcomposite structure, shielding the structure, magnetic the field magnetic of the nonworking field of the areanonworking above the area aboveareareceiving abovethe receiving the coil receiving is lowered coil coil whileis islowered lowered the magnetic while fieldthe the magnetic ofmagnetic the working field field of area the of working is the enhanced. working area is enhanced. area is enhanced.

(a) Single shield (b) Double shield (c) Composite shield

Figure (a6.) SingleSimulated shield magnetic flux density(b) Doubledistribution shield in a cross-section(c) ofComposite different types shield of magnetic coupler. Figure 6.Figure Simulated 6. Simulated magnetic magnetic flux flux density density distribution distribution in in a across-section cross-section of di ff oferent different types of types of magnetic coupler. magneticIn ordercoupler. to suppress the influence of the electromagnetic field produced by the coil on the circuit Inboard, order it to is suppress necessary the to influence know the of radial the electromagnetic nonworking area field flux produced density by at the 10 coilmm on above the circuit the Inreceiving orderboard, itto coil, is suppress necessary and in order to the know to influence suppress the radial the of nonworking radiatio the electroman effect area of flux thegnetic densitymagnetic field at field 10 produced mm on abovethe human the by receiving thebody, coil on the circuit consideringboard,coil, and it inis the order necessary packaging to suppress toof theknow the products radiation the radialand effect the of nonus theer’sworking magnetic habits, the fieldarea simulate on flux thed humandensity measuring body, at position considering10 mm is above the 250 mm from the center of the magnetic coupler to the outer axis of the magnetic coupler. The receivingthe coil, packaging and in of order the products to suppress and the the user’s radiation habits, the effect simulated of the measuring magnetic position field is on 250 the mm human from body, schematic diagram is shown in Figure 7. consideringthe center the packaging of the magnetic of the coupler products to the outerand axisthe ofuser the’ magnetics habits, coupler.the simulated The schematic measuring diagram position is is shown in Figure7. 250 mm from the center of the magnetic coupler to the outer axis of the magnetic coupler. The schematic diagram is shown in Figure 7.

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250mm 10mm10mm 250mm

(a()a ) (b(b) )

FigureFigure 7. 7. SchematicSchematic Schematic diagramdiagram diagram ofof of simulated simulated simulated measurement measurement measurement position. position. position. (a )( a Radial()a )Radial Radial position position positio 10n mm10 10 mm abovemm above above the receivingthethe receiving receiving coil. coil. (coil.b) Axial( b(b) )Axial Axial position position position 250 250 mm 250 mm outsidemm outside outside the magneticthe the magnetic magnetic coupler. coupler. coupler .

AsAs shown shown inin in FigureFigure Figure8 ,8, from8, from from −68 68−68 mm mm mm to to to 68 68 68 mm mm mm is is theis the the working working working area area area of magneticof of magnetic magnetic coupler. coupler. coupler When .When W thehen − coilthethe coil is coil not is is shielded,not not shielded, shielded, the maximum the the maximum maximum magnetic magnetic magnetic flux density flux flux density densit at 10 mmy at at 10 10 above mm mm above the above coil the isthe 1.519coil coil is mT,is 1.519 1.51 the 9mT, mutualmT, the the inductancemutualmutual inductance inductance between between thebetween coils the is the 19.2 coils coilsµH, is is and19.2 19.2 theμ μH,H coupling and, and the the coecoupling couplingfficient coefficient iscoefficient 0.317. Due is is 0.317. to0.317. the Due poorDue to constraintto the the poor poor onconstraintconstraint the magnetic on on the the field, magnetic magnetic the magnetic field, field, the the field magnetic magnetic in the nonworkingfield field in in the the nonworking areanonworking is still very area area strong. is is still still very When very strong. strong. ferrite When isWhen not addedferriteferrite is directly is not not added added above directly directly the receiving above above the coil, the receiving thereceiving maximum coil, coil, the magneticthe maximum maximum flux magnetic densitymagnetic at flux 10flux mm density density above at at the10 10 mm coilmm isaboveabove 2.556 the the mT. coil coil is is 2.556 2.556 mT. mT.

(a()a ) (b(b) ) 2.5 Ferrite+0.1mmAluminium Ferrite+1mmAluminium Ferrite+2mmAluminium 2 Ferrite+3mmAluminium

1.5

0.5 Magnetic Flux Density/mT

0 -150 -100 -50 0 50 100 150 Distance/mm (c()c ) (d(d) )

FigureFigure 8. 8. Magnetic MagneticMagnetic flux fluxflux density density density versus versus versus simulated simulated measurement measurement position position position at at at radial radial 10 10 mm mm above above receivingreceiving coil. coil. coil. ( a((a)a ))No NoNo shielding. shielding.shielding. ( b( (b)b )Single) Single Single shield shield shield magnetic magnetic magnetic coupler coupler coupler with with with different different different ferrite ferrite ferrite thickness. thickness. thickness. (c ()c ) (DoublecDouble) Double shield shield shield magnetic magnetic magnetic coupler coupler coupler with with with different different different aluminum aluminumaluminum thickness. thickness. thickness. ( d ((dd) ))Comparison Comparison Comparison of ofof different di differentfferent shieldingshielding types. types .

WhenWhen ferrite ferrite is is added added along along the the flux flux path, path, the the ma magneticgnetic domain domain of of ferromagnetic ferromagnetic material material will will movemove because because of of its its high high conductivity conductivity (relative (relative permeability permeability 2800 2800 H/m)H/m) and and small small magnetic magnetic resistance,resistance, and and the the magnetic magnetic field field generated generated by by current current will will be be applied applied to to ferromagnetic ferromagnetic material material as as

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When ferrite is added along the flux path, the magnetic domain of ferromagnetic material will move because of its high conductivity (relative permeability 2800 H/m) and small magnetic resistance, and the magnetic field generated by current will be applied to ferromagnetic material as an external magnetic field, which will increase the magnetic domain consistent with the magnetic field; and decrease the magnetic domain which is inconsistent with the direction of magnetic field, thus, forming a strong magnetization vector and its induced magnetic field. A large amount of flux in the air passes through ferrite, resulting in a decrease in the flux leakage in the air. Because of the high permeability of Ferrite, the flux lines in the air are attracted to the Ferrite in large quantities. Additionally, because of the existence of aluminum, the magnetic lines cannot penetrate through the aluminum plate and can only gather around the edge of the ferrite, which results in the high flux density of the edge of the magnetic coupler. The smaller the flux in the air, the better the shielding effect of the magnetic coupler. As shown in Figure8, as far as the single layer shielding structure is used above the receiving coil, the magnetic shielding effect using 5 mm ferrite core is best, but not much different from that of using 2.5 mm ferrite. Considering the cost, weight, and volume, the design requirements can be met by using 2.5 mm ferrite. As the ferrite thickness increases, the shielding effect increases slowly. The shielding effect of double shield is better than that of single shield, but the addition of aluminum plate will lead to the decrease of mutual inductance and coupling coefficient. The choice of aluminum plate thickness is not the thicker the better. The thinner the aluminum plate, the worse the shielding effect; and the thicker the aluminum plate, the slower the shielding effect enhancement. Table3 shows the parameters of different types of shielding structures.

Table 3. Parameters of diﬀerent types of shielding structure for receiving coil.

Magnetic Coupler Parameter Value single shield magnetic coupler ferrite thickness 2.5 mm ferrite thickness 2.5 mm double shield magnetic coupler aluminum plate thickness 2 mm ferrite thickness 1 mm composite shield magnetic coupler nanocrystalline strips 26 µm aluminum foil thickness 0.1 mm

Due to the ultra-high permeability of nanocrystalline materials (relative permeability of 8000 H/m), a large amount of magnetic flux in the air is attracted by nanocrystals to the working area, which reduces the magnetic flux in the nonworking area and reduces the influence of aluminum foil on the mutual inductance of magnetic couplers. Figure9 shows the magnetic flux density versus simulated measurement position at axial 250 mm outside the magnetic coupler. The working frequency of the magnetic coupler studied in this paper is 20 kHz, and, under this frequency, the limit value of the flux density of the public exposed to time-varying electromagnetic fields is 27 µT. From the simulation results, the thickness of magnetic couplers with single shielding structure has no obvious effect on the shielding effect, and the use of single shielding structure cannot meet the requirements of the guidelines for limited time-varying electric and magnetic field exposure issued by ICNIRP in 2010 [17]. For the magnetic couplers with double shielding structure, the thinner the aluminum plate is, the better the effect is. This is because the existence of the aluminum plate hinders the path of the magnetic flux line, which makes the magnetic flux line gather at the edge of the aluminum plate, resulting in a large flux density in air. The maximum flux density of the composite magnetic coupler in the working area is 24.2 µT, which meets the limit requirements of ICNIPR 2010. Energies 2019, 12, x FOR PEER REVIEW 8 of 12

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(a) (b)

(c)

FigureFigure 9.9. MagneticMagnetic fluxflux densitydensity versusversus simulatedsimulated measurementmeasurement positionposition at axialaxial 250250 mmmm outsideoutside thethe magneticmagnetic coupler. coupler. ( a()a Single) Single shield shield magnetic magnetic coupler coupler with w diithfferent different ferrite ferrite thickness. thickness. (b) Double (b) Double shield magneticshield magnetic coupler coupler with di ffwitherent different aluminum alumin thickness.um thickness. (c) Comparison (c) Comp of diarffisonerent of shieldingdifferent types.shielding types. The data in Table4 show that the magnetic lines in space diverge in all directions without shielding, and theThe flux data density in Table at the 4 show measured that the position magnetic is small. lines Only in space after diverge adding in ferrite all directions to the side without of the transmittingshielding, and coil the is flux most density of the flux at the in themeasured air concentrated position is around small. theOnly working after adding area through ferrite to the the ferrite side ofof thethe transmittingtransmitting coil,coil is while most the of receivingthe flux in coil the has air noconcentrated ferrite guiding around the magneticthe working field, area so through the flux densitythe ferrite above of the the transmitting magnetic coupler coil, while is high. the receiving The shielding coil h easffect no offerrite the single guiding shielding the magnetic structure field, is increasedso the flux by density 33.02% above at 10 the mm magnetic above the coupler receiving is high. coil andThe 2.33%shielding at 250 effect mm of outside the single the magneticshielding coupler.structure The is increased coupling by coe 33.02fficient% isat increased10 mm above by 45.11% the receiving with respect coil and to the 2.33% magnetic at 250 couplermm outside without the shielding.magnetic coupl The shieldinger. The coupling effect at 10 coefficient mm above is the increased receiving by coil 45.11% and 250with mm respect outside to the magnetic magnetic couplercoupler are without improved shielding. by 61.22% The and shielding 16%, respectively, effect at 10 by mm using above double the receivingshielding structure, coil and 2 and50 mm the couplingoutside the coe ffi magnetcient isic increased coupler are by 29.33%. improved The by shielding 61.22% e andffect 16 at% 10, respectively mm above the, by receiving using double coil is increasedshielding bystructure, 54.8% and and that the atcoupling 250 mm coefficient outside the is magnetic increased coupler by 29.33%. is increased The shielding by 19.33%, effect and at the 10 couplingmm above coe thefficient receiving is increased coil is increased by 39.11% by by 54.8 using% theand composite that at 250 shielding mm outside structure. the magne Comparedtic coupler with theis increased axial shielding by 19.33 eff%ect, and of the the magnetic couplingcoupler, coefficient the is shielding increased eff byect 39.11% above theby using magnetic the composite coupler is moreshielding obvious structure. after using Compared flat magnetic with the shielding. axial shielding In terms effect of shielding of the magnetic effect, the ecoupler,ffect of thethe composite shielding shieldingeffect above structure the magnetic is significantly coupler better is more than obvious that of the after single using shielding flat magnetic structure. shielding Compared. In terms with the of doubleshielding shielding effect, the structure, effect of the the shielding composite eff ectshielding of the double structure shielding is significantly structure better at the than radial that position of the 10single mm shielding above the structure. receiving coilCompared is slightly with better the double than that shielding of the composite structure, shielding the shielding structure, effect but of the compositedouble shielding shielding structure effect isat better the radial in terms position of the 10 improvement mm above the of receiving the coupling coil is coe slightlyfficient. better than

Energies 2019, 12, x FOR PEER REVIEW 9 of 12 that of the composite shielding structure, but the composite shielding effect is better in terms of the improvement of the coupling coefficient.

Table 4. Data of different magnetic coupling structures.

The Maximum Radial Maximum Axial EnergiesShielding2019, 12, 3000 Flux Density of 10 Flux Density of Mutual Coupling9 of 12 Type mm above the Magnetic Couplers Inductance/μH Coefficient ReceivingTable 4.Coil/mTData of diﬀerentin magnetic 250 mm/ couplingμT structures. Magnetic coupler The Maximum Radial Maximum Axial Flux1.519 Density of 10 Flux27.4 Density of Mutual19.2 Coupling0.317 withoutShielding Type mm above the Magnetic Couplers Inductance/µH Coeﬃcient shielding Receiving Coil/mT in 250 mm/µT Non-shield on Magnetic coupler 2.5561.519 30 27.4 19.237.5 0.3170.408 receivingwithout shieldingcoil SingleNon-shield shield on 1.712 29.3 57.1 0.460 2.556 30 37.5 0.408 Doublereceiving shield coil 0.991 25.2 46.8 0.410 Single shield 1.712 29.3 57.1 0.460 Composite Double shield1.155 0.991 24.2 25.2 46.853.9 0.4100.441 Compositeshield shield 1.155 24.2 53.9 0.441

The layers of nanocrystals of the composite structure are optimized, and the magnetic coupler The layers of nanocrystals of the composite structure are optimized, and the magnetic coupler composed of two, four, six, and eight layers of nanocrystalline materials is modeled and simulated. composed of two, four, six, and eight layers of nanocrystalline materials is modeled and simulated. Similarly, the magnetic flux density distribution at the radial direction of 10 mm above the receiving Similarly, the magnetic flux density distribution at the radial direction of 10 mm above the receiving coil is obtained from the simulation results, as shown in Figure 10. The shielding effect of the coil is obtained from the simulation results, as shown in Figure 10. The shielding effect of the composite composite magnetic shielding structure with two, four, six, and eight layers of nanocrystals magnetic shielding structure with two, four, six, and eight layers of nanocrystals increases by 52.46%, increases by 52.46%, 54.81%, 55.56%, and 55.71%, respectively, at the radial 10 mm above the 54.81%, 55.56%, and 55.71%, respectively, at the radial 10 mm above the receiving coil. The shielding receiving coil. The shielding effect of the eight-layer nanocrystalline structure in the working area is effect of the eight-layer nanocrystalline structure in the working area is slightly better than that of slightly better than that of the other multilayered nanocrystalline structure, but the shielding effect the other multilayered nanocrystalline structure, but the shielding effect at the edge of the magnetic at the edge of the magnetic coupler is the same as that of the four-layer nanocrystalline structure. For coupler is the same as that of the four-layer nanocrystalline structure. For axial results, the number of axial results, the number of nanocrystalline layers has little effect on the magnitude of magnetic flux nanocrystalline layers has little effect on the magnitude of magnetic flux density. Therefore, in order to density. Therefore, in order to save cost, the four layers of nanocrystalline structure should be save cost, the four layers of nanocrystalline structure should be chosen. chosen.

(a) (b)

FigureFigure 10.10. MagneticMagnetic ﬂuxflux densitydensity versusversus simulatedsimulated measurementmeasurement position.position. ((aa)) RadialRadial 1010 mmmm aboveabove receivingreceiving coil.coil. ((bb)) AxialAxial 250250 mmmm outsideoutside thethe magneticmagnetic coupler.coupler.

4.4. ExperimentalExperimental ValidationValidation InIn orderorder toto verifyverify thethe ﬁnitefinite elementelement simulationsimulation results,results, thisthis paperpaper takestakes thethe magneticmagnetic couplercoupler ofof thethe compositecomposite shieldingshielding structurestructure inin thethe simulationsimulation asas anan exampleexample andand producesproduces thethe experimentalexperimental model,model, asas shown shown in in Figure Figure 11 11.. Among Among them, them, the the switching switching frequency frequency is 20is 20 kHz, kHz, output output power power is 450 is 450 W, and the load resistance is 136 Ω, which is obtained by impedance matching and is the optimal load of the magnetic coupler. Energies 2019, 12, x FOR PEER REVIEW 10 of 12

W, and the load resistance is 136 Ω, which is obtained by impedance matching and is the optimal Energies 2019, 12, 3000 10 of 12 load of the magnetic coupler.

Drive supply Oscilloscope

Load

Transmitting circuit

Receiving Gaussmeter circuit

Magnetic coupler Energies 2019, 12, x FOR PEER REVIEW 10 of 12

W, and the load resistance Figureis 136 11.Ω, Experimentalwhich is obtained setup of by the impedance WPT system. matching and is the optimal load of the magnetic coupler.Figure 11. Experimental setup of the WPT system. The experimental coil is wound by Litz wire, and a composite shielding layer is formed using m μ μ μ μ 400V / 2 1000 v / -28.40s / -20.00 s / 500V / 2 300V / -28.40s / -20.00s / a 1 mm thick MnZn ferrite, 4 layers of nanocrystals, and 0.1 mm thick aluminum foil for the coil uCp to form a composite shieldingDrive supply magnetic coupler. As shown in FigureOscilloscope 12a, iLp is the current flowing ugs uds through the transmitting coil and uCp is the voltage across the compensation capacitor in parallel with Load the transmitting circuit. In this paper, a single switching resonant converter is used. The P-S type of reactive power compensationTransmitting circuit uses parallel compensation on the primary side and series compensation on the secondarycircuit side. As the equivalent input power supply on the primary side is not iLp a pure sinusoidal, the shape of the primary side current is not a sinusoidalReceiving wave too. As shown in Figure 12b, ugs is theGaussmeter switching transistor driving voltage, and uds is thecircuit voltage between the drain and the source. Before the switch control signal ugs comes, the voltage uds between the drain and source of the switch has been reduced to zero, achieving zero voltage turn-on and reducing switching losses. At the resonant(a) frequency, the approximate value of the (DC-DC)(b) efficiency of the whole system is obtained by using the oscilloscope to measure and calculate the voltage and current on the originalFigure 12. rectifier Experiment module results. and (a the) Current load. and The voltage efficiency waveforms of the WPTof transmitting system with circuit. single (b) Drive shielding voltage and voltage waveform between drain and source. Magnetic magnetic couplers is 79%, the efficiency of the WPT system with doublecoupler shielding magnetic couplers is 68%, and the efficiency of the WPT system with composite shielding magnetic couplers is 87%. The experimental coil is wound by Litz wire, and a composite shielding layer is formed using a Therefore, the composite structure magnetic couplers can effectively improve the efficiency of the 1 mm thick MnZn ferrite, 4 layers of nanocrystals, and 0.1 mm thick aluminum foil for the coil to magnetic couplers under theFigure circuit 11. parameters. Experimental setup of the WPT system. form a composite shielding magnetic coupler. As shown in Figure 12a, iLp is the current flowing through them transmitting coil andμ uCp μ is the voltage across the compensation capacitorμ inμ parallel 400V / 2 1000 v / -28.40s / -20.00 s / 500V / 2 300V / -28.40s / -20.00s / with the transmitting circuit. In this paper, a single switching resonant converter is used. The P-S uCp type of reactive power compensation circuit uses parallel compensation on the primary side and ugs uds series compensation on the secondary side. As the equivalent input power supply on the primary side is not a pure sinusoidal, the shape of the primary side current is not a sinusoidal wave too. As shown in Figure 12b, ugs is the switching transistor driving voltage, and uds is the voltage between the drain and the source.iLp Before the switch control signal ugs comes, the voltage uds between the drain and source of the switch has been reduced to zero, achieving zero voltage turn-on and reducing switching losses. At the resonant frequency, the approximate value of the (DC-DC) efficiency of the whole system is obtained by using the oscilloscope to measure and calculate the voltage and current on the original rectifier module and the load. The efficiency of the WPT system with single shielding magnetic couplers(a) is 79%, the efficiency of the WPT system(b) with double shielding magnetic couplers is 68%, and the efficiency of the WPT system with composite shielding magnetic Figure 12.12. ExperimentExperiment results. (a) Current and voltagevoltage waveformswaveforms ofof transmittingtransmitting circuit.circuit. (b) Drive voltage and voltage waveformwaveform betweenbetween draindrain andand source.source.

The experimental coil is wound by Litz wire, and a composite shielding layer is formed using a 1 mm thick MnZn ferrite, 4 layers of nanocrystals, and 0.1 mm thick aluminum foil for the coil to form a composite shielding magnetic coupler. As shown in Figure 12a, iLp is the current flowing through the transmitting coil and uCp is the voltage across the compensation capacitor in parallel with the transmitting circuit. In this paper, a single switching resonant converter is used. The P-S type of reactive power compensation circuit uses parallel compensation on the primary side and series compensation on the secondary side. As the equivalent input power supply on the primary side is not a pure sinusoidal, the shape of the primary side current is not a sinusoidal wave too. As shown in Figure 12b, ugs is the switching transistor driving voltage, and uds is the voltage between the drain and the source. Before the switch control signal ugs comes, the voltage uds between the drain and source of the switch has been reduced to zero, achieving zero voltage turn-on and reducing switching losses. At the resonant frequency, the approximate value of the (DC-DC) efficiency of the whole system is obtained by using the oscilloscope to measure and calculate the voltage and current on the original rectifier module and the load. The efficiency of the WPT system with single shielding magnetic couplers is 79%, the efficiency of the WPT system with double shielding magnetic couplers is 68%, and the efficiency of the WPT system with composite shielding magnetic

Energies 2019, 12, x FOR PEER REVIEW 11 of 12

Energiescouplers2019 ,is12 87%., 3000 Therefore, the composite structure magnetic couplers can effectively improve11 of the 12 efficiency of the magnetic couplers under the circuit parameters. As shown in the Figure 13, the 10 mm radial flux density curve above the coil and the 250 mm As shown in the Figure 13, the 10 mm radial flux density curve above the coil and the 250 mm axial flux density curve of the magnetic coupler are received. Due to the influence of the axial flux density curve of the magnetic coupler are received. Due to the influence of the experimental experimental environment, there is a slight error between the test results and the simulation results. environment, there is a slight error between the test results and the simulation results.

26 Simulation Experiment

T 24 μ

Magnetic Flux Density/ 16

14 -100 -75 -50 -25 0 25 50 75 100 Distance/mm (a) (b)

FigureFigure 13. 13.Magnetic Magnetic flux flux density density versus versus distance distance of experiment of experiment and simulation and simulation comparison. comparison. (a) Radial (a) positionRadial position 10 mm above 10 mm the above receiving the receiving coil with coil composite with composite shielding shielding coupler on coupler receiving on receiving coil coupler. coil (bcoupler.) Axial 250(b) mm Axial outside 250 themm magnetic outside couplerthe magnetic with composite coupler with shielding composite coupler shielding on receiving coupler coil. on receiving coil. 5. Conclusions 5. ConclusionsIn this paper, the finite element analysis of the magnetic coupling mechanism of the wireless powerIn transfer this paper, system the is carriedfinite element out, and analysis the magnetic of the flux magnetic density coupling distribution mechanism of the magnetic of the couplerwireless ispower obtained. transfer The magneticsystem is shieldingcarried out, of theand composite the magn shieldingetic flux density structure distribution and the traditional of the magnetic single shieldingcoupler is structure obtained. and The double magnetic shielding shielding structure of the composite are compared shielding and analyzed. structure and The the results traditional show thatsingle the shielding maximum structure radial nonworking and double area shielding flux density structure at 10 are mm compared above the and receiving analyzed. coil The decreases results fromshow the that original the maximum 2.556 mT toradial 1.155 nonworking mT, the axial area nonworking flux density area at maximum 10 mm above flux density the receiving at 250 mm coil outsidedecreases the from magnetic the original coupler 2.556 decreases mT to from1.155 themT, original the axial 30 nonworkingµT to 24.2 µarT,ea the maximum leakage flux flux density in the nonworkingat 250 mm outside area decreases the magnetic obviously, coupler the magnetic decreases flux from in thethe working original area30 μ isT etoffectively 24.2 μT, constrained, the leakage theflux mutual in the inductancenonworking of area the magneticdecreases couplingobviously, mechanism the magnetic increases flux in by the 2.8 working times, and area the is effectively coupling coeconstrained,fficient increases the mutual by 39.11%. inductance The e offfi ciencythe magnetic of the systemcoupling is 87%.mechanism At the sameincreases time, by the 2.8 composite times, and shieldingthe coupling structure coefficient is optimized, increases andby 39.11%. the composite The efficiency shielding of the magnetic system coupleris 87%. At with the four same layers time, ofthe nanocrystalline composite shielding structure structure is selected is optimized, considering and the the shielding composite eff shieldingect and cost. magnetic The experimental coupler with verificationfour layers is of carried nanocrystalline out. Compared structure with theis selected traditional considering magnetic shieldingthe shielding structure, effect theand composite cost. The structureexperimental magnetic verification couplers is carried are only out. 75% Compared of the traditional with the magnetictraditional couplers, magnetic and shielding the aluminum structure, contentthe composite is only structure 5% of the magnetic traditional couplers magnetic are couplers.only 75% of The the shielding traditional eff magneticect is slightly couplers, better and than the thealuminum traditional content shielding is only structure, 5% of itthe is flexibletraditional and ma easygnetic to operate, couplers. and The it can shielding be used effect in any is kindslightly of shieldingbetter than structure. the traditional shielding structure, it is flexible and easy to operate, and it can be used in any kind of shielding structure. Author Contributions: Methodology, H.X. and C.W.; Software, H.X.; Validation, H.X. and Y.L.; Formal Analysis, H.X.;Author Investigation, Contributions: H.X. and Methodology, D.X.; Writing-Original H.X. and DraftC.W.; Preparation, Software, H.X.; Writing-ReviewValidation, H.X. & Editing,and Y.L.; C.W. Formal and D.X..;Analysis, Visualization, H.X.; Investigation, H.X. and Y.L.; H.X. Supervision, and D.X.; C.W.; Writing-Original Project Administration, Draft Preparation, C.W.; Funding H.X.; Acquisition,Writing-Review C.W. & Funding:Editing, C.W.This researchand D.X..; was Visualization, funded by NationalH.X. and NaturalY.L.; Supervision, Science Foundation C.W.; Project of China Administration, grant number: C.W.; 51877113. Funding AndAcquisition, The APC C.W. was funded by National Natural Science Foundation of China.

ConﬂictsFunding: of This Interest: researchThe was authors funded declare by National no conﬂicts Natura of interest.l Science Foundation of China grant number: 51877113. And The APC was funded by National Natural Science Foundation of China. References Conflicts of Interest: The authors declare no conflicts of interest. 1. Wang, C.S.; Covic, G.A.; Stielau, O. Investigating an LCL load resonant inverter for inductive power transfer Referencesapplications. IEEE Trans. Power Electron. 2004, 19, 995–1002. [CrossRef]

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